Internet disconnects after a while in P2P

I seem to be having a problem with my desktop computer with a broadcom gigabit ethernet card.
I have the new Router Thomson tg787.
In my HP laptop connected through wireless or cable, everything goes fine with web surfing and P2P programs, including uTorrent and emule, the connection never drops and keep up with good speed.
My desktop connects through a network adapter Broadcom Gigabit Ethernet netextreme: after some time on, with good speed (may be only a few minutes in P2P) it drops the connection and I have to restart the computer because, in network connections, there's no use trying to repair it...
Leaving the internet connected with only a web page (for example a newspaper webpage) the connection stay ok.
I already updated the drivers and also used a software (TCP optimizer) but it's all the same.
I believe that there is nothing wrong with the router and the cables, since the laptop with the same connection and router and in P2P, stays always connected.
Moreover, I have another modem / router Dlink previously installed with which I noted the same problem ...
The desktop is a pentium 4, 3,01 Ghz with 1.5 mega RAM and Windows XP SP3.
Please can anybody give me some hint?