If I start my PC today then it starts normally and works fine. However, if I shut it down and restart it on the same day it gives 3 long beeps and a blank screen. If I shut it down and restart it the next day it starts normally.
It sounds to me like there could be a problem with your graphics card. During the boot up process, if the BIOS encounters an error, it will send the output to the graphics card for display. If no graphics card is detected, the BIOS will give multiple beeps to represent an error state. What the beep sequence means is contingent on the BIOS software on your computer. I'd start with finding the BIOS manufacturer and searching for Beep Error Codes.
I would assume that the fact that you 'wait one day' is really a by product of some form of electrical discharge or leaking that occurs when the system is being shut down.
Try this-- cut off the PC. Unplug the power cable, press the power button for 5 seconds, plug the PC back in, and try and cut it on again. My assumption is your PC will magically start working. This, obviously, doesn't fix the underlying problem but it will get your PC up and running much more quickly.
Diagnosing the specific problem may be a bit difficult. If you live near a PC shop with a decent return policy, I'd buy and swap out parts one at a time trying to find the broken piece of hardware. First, I'd start with the power supply, followed by the graphics card and then the motherboard.
Hope it helps.