I'm going to suggest you check out my answer to Computer won't stay powered up. It is a different base problem but many of the steps I list out still apply. I will quote it extensively below with some modification specific to your setup. Scan over this first before following the steps. It could be as simple as your motherboard's on-board video taking precedence over the Radeon and not hearing the beep because the PC speaker isn't plugged in. If you can, attach a monitor to the on-board video with the Radeon removed and see if anything comes up. If you can't...
Let's get to the basics:
- Unplug your machine
- Disconnect all of your drives from your motherboard (we don't care about booting right now, we just want it to POST and stay on--hibernate is not the issue) I mean everything, HDDs, optical drives, floppy (if you have one), unplug it all from the motherboard.
- Also, remove all of your add-in cards including your video card.
- Remove all of your RAM except for 1 module and make sure that's in the primary slot (DDR1 or something silkscreened on the board).
- Unplug everything both internal and external from your computer including power, monitor cable, and keyboard, power and reset switches, internal speaker... (really, everything else--mouse, USB things, audio--it makes life much easier).
You should now have a motherboard with a processor, and a stick of ram. That's it. At this point I also would like you to un-plug your power connections. Check to make sure your ram is seated correctly, did the little side tabs lock into place? Good.
Now I would like you to plug in the 24-pin power connection (I know you've not yet removed it because it's in there correctly, but just humor me, pull it out and then plug it back in). The locking tab on the 24-pin power should be towards the outside of the motherboard and the plug should be flush with the receptacle. There should be no empty holes in that connector. Also plug in the 4-pin CPU power and make sure it's the correct one, the locking mechanism for that plug should also be facing the edge of the motherboard.
Attach your keyboard to the appropriate port (USB or PS2). And connect the monitor via the onboard video. If your monitor won't work with the VGA port just leave it disconnected. Now find your internal speaker and attach it to the appropriate pins over by your SATA ports (it should say PC SPKR or something silk-screened there).
At this point there should only be power, monitor, keyboard and PC speaker attached to the motherboard (and the power is unplugged at the power supply).
Reset the CMOS, it looks to be the jumper near your SATA connectors, but check your manual. While resetting it let the jumper sit for a while. Now, remove your battery. Walk away, make some tea (remember power is unplugged for this). While your tea is brewing, have some cheese toast, you don't need this much time, but it will allow you to relax. Take some deep soothing breaths.
Now, check all your power connections. Yup, I know you just put those there, but check them anyway.
Pop the battery back in and plug the power supply into the wall. Make sure the switch on the power supply has the line down.
Now to turn it on. You can't because you don't have the power switch on the case plugged in. If you're confident that is not the problem, go ahead and plug it in. Or you can take a trusty screwdriver, coin, olympic gold medal, or other conductive material and short the two power switch pins on that chassis header next to your SATA ports.
Does it do anything? Does it beep? If you don't have a monitor connected and it beeps one short beep that's good. If you can see wonderful booting things, hooray!
If it does nothing, that is bad.
At this point we have a Choose Your Own Adventure story. If things are good go to the section labeled "Huzzah!" below. If things are going bad go to the "le sad" section below. When adding or removing components make sure that the power is off to your computer before proceeding (if you don't un-plug the computer at least switch the power supply to "off").
You know your base system works at this point. Turn off the computer and plug in the rest of your chassis header things and reboot it, just to make sure one of them aren't fouling things up.
It still works, yes?
Remember, turn off the computer before adding components.
Good, let's start with say, more memory, because if at bare-bones it works, memory will probably break it (not because your memory is bad, just because sometimes things are wonky). Does it still work with your memory? All of it? If not, go back to one stick and enter the BIOS, set the memory voltage and timings to the manufacturer recommended settings.
Okay, so you're loaded up with your memory and CPU, now lets get that video card in there. Insert it into the longest blue slot labeled "PCI-EX16" (I know probably know this, but others may not and find this helpful). I do not believe that any of the 4670's required external power, but if yours does, make sure to attach that.
You should make sure the card is pushed all the way down, many people don't get their cards in all of the way with the first few times of building their computer. You should probably lock it in place, those fan reverberations can wiggle things loose. Make sure it's screwed down as well.
Does it still boot? If so, that's good, now attach the rest of the items one by one, powering off in between adding an additional component. You'll either track down the problem or not. If it works with everything connected, congratulations you fixed it!
If after adding your video card it doesn't boot a couple of things could be happening.
- A bad video card
A bad motherboard (you already tested this with the second motherboard)
- Not enough power! (unlikely given your power supply)
Try using the card in a different system to rule out #1. You could/should also borrow someone's card to try it in your board.
- Swap that stick of memory for the other one (check to see if it's still a problem)
- Now, at this point your fans should be clear, and your heatsinks look like new, right?
This is where you are left with few culprits. It could be your processor or
motherboard (both mostly unlikely, the motherboard especially since you tried a second one). It could be a heat issue (most probable) or an issue with your powersupply (possible), short in the keyboard (I've seen it), short in the monitor cable (seen it), short in the power cable (this involves fires and melting, you should notice that). In order I would try the following:
- swap out power cable, keyboard, monitor (one at a time, in that order, because you probably have a bunch of power cables, and probably fewer of the other two)
- remove heatsink from processor, clean processor top and heatsink until your heatsink looks new. apply thermal paste (remember a very small amount). Cod liver cream, or zinc oxide sunscreen work for a very temporary, risky fix (not recommended). reseat everything careful here, if you've not done it before, read up and call a buddy, it's easy to snap things off of the heatsink, and forcing the CPU with ruin your day.
- swap out the power-supply
- find a buddy with a compatible motherboard and either try your chip in his board, or his chip in yours, try again.
- remove the motherboard from the case, and the powersupply, set it up on a hunk of plywood after wiping it down. shake the empty case out. run stuff with the motherboard sitting on the plywood.
- request additional help on superuser in this question