I read the other post you linked to. If your router does not support 1:1 NAT then you have two options:
Use the router as a router and not a NAT device. On the config page you can turn off NATting. You then assign 1 public IP to the router itself on it's LAN interface with the correct subnet (this info will come from your ISP). Then you assign the other public IP's directly to the machines you want accessible on the internet.
On one of these machines add a second NIC and configure it with ICS or RRAS to do the NAtting for the other machines that will have private IP's only (otherwise they cannot route out to the internet). Wire the machines with public IP's to your router and wire your machines with private IPs to a separate router/switch to the 2nd NIC on the machine that will act as the NAT device for other PC's. For the machine acting as the NAT I would advise using the one which is the DNS, DHCP server so this can assign IP's out.
Buy a rotuer that supports one to one NAT.
You never said what you want to access on the PC's on the internet? If it is simply remote desktop for example you can set a different port for each PC then port forward through to them with one public IP using your current set up. You can now access every PC on the internet but on one IP instead.
I am assuming you have a certain amount on knowledge but if you don't understand any of that, ask away and I will expand on it.
For solution 1 above, from the link you posted http://dslwebserver.com/main/fr_index.html?/main/diagram-Multiple-IP-addresses-with-Router-and-Private-LAN.html all the computers that have blue arrows are the PC's I said will be connected to the router directly with public IP's (like diagram). Where the web server has a red arrow indicating it has a second NIC which connects to the LAN non of yours will do this except the one acting as the NAT device. The server acting as the NAT device will serve the same function as the device called "NAT/router..." which is on both networks and then two PC's sit behind it. The 2 PC's sat behind this device (which would be your server) will be all your private PC's.
Solution 1 presents its own problems however because if you want to connect to file shares to the machines with public IP's you need to open this up on the firewall. This also means anyone on the internet can potentially connect as well. You can get round this with extensive firewall configuration but for the hassle involved you are probably better just getting a 1:1 NAT router.