Run a test:
Remove the router from the equasion. Try connecting to the Internet directly with each PC, and use your browser to connect to the web page in question. Do you lose your connection in either case? If you do, the PC is at fault (so far). If you don’t lose the connection, the router may be at fault.
Now connect the router, and then one PC to the first port connect on the router. Try and make that broswer connection again. Yes? No?
Switch to the second port connection. Repeat above. Yes? No?
Now switch PCs and run the two previous examples. Yes? No?
Now connect both PCs to the router and repeat. Yes? No?
Swap the two PC port connects on the router. Repeat again.
The object is to test each piece of hardware in a systematic fashion to rule oue/rule in potential culprits. You still need to repeat the entire process with a different broswer. Assuming you are using IE, try again with Netscape and Opera. That way you also test your broswer, as well as the hardware.
Lost? Pay your bill with a check, an envelope and a stamp.