What was the last thing you did to the machines, as this is usualy the reason things go wrong.
A router cannot disable the security itself, have you pressed the reset button on the router?
As wep is very weak there is a chance someone has broke in and fiddled.
WPA- PSK is certainly a lot more secure, and yes the Linksys WMP54G uses WPA too.
Keep reseting either router/computer will not fix the problem.
First make sure you can view web pages with an ethernet cable first then go into the network setting and make sure the Pre-shared keys (password) are the same, the router is broadcasting the SSID and the IP addressing on the wireless card is set to automatic.
As for connection speed, they should be the same for WEP and WPA. Would be a good idea to contact your ISP as there may be some setting in the router that needs changing.