The problem you're experiencing is almost certainly related to the router. It's not just Linksys, and it's not that the router's "broken" at all. It's being killed by connections. What's opening all the connections? Your bittorrent client.
Here's the deal:
"The default firmware for Linksys and most router track old connections for FIVE days then started to clear dead connection, which causes the router to hang when using P2P apps, or any software that generates a lot of connections which the router can't take. DHT only aggravates the situation because of the number of connections it generates."
"Linksys has yet to address this issue due to some reason, but there is a fix. If you use alternative WRT54G firmware, you can put in a start-up script to fix this problem."
The only fix you can really put in place is alternative firmware on the router. I wouldn't do that if you're a n00b.
My info comes from quite a while looking into this for my own, same, problem with my WRT54G.
Here's the link to where I finally nailed down the most info in one place:
http://forums.hardwarezone.com/showthread.php?t=998127
This is more info on alternative firmware:
http://lifehacker.com/software/route...ter-178132.php
This is in case you decide to try it:
http://www.dd-wrt.com/wiki/index.php...ported_Devices
The guide covers many brands and models of router.
Best of luck!