Wireless can be a pain like this - my Belkin router and card is just the same, especially the seeing but refusing to connect thing. It may be as simple as 'stopping' the wireless card, ejecting it and reinserting it in the slot. That should force the thing to re-acquire its connection to the wireless network from scratch.
If that solves the problem, then the likely root cause is poor signal strength from the router. Check that it is sited properly for good coverage, and try changing the broadcast channel ('fraid I can't advise you how to do this on a Linksys, but if you can access the router config screen it should be pretty easy). Cordless phones, baby monitors and low-wattage light bulbs can all affect the signal if they get too close. I have heard it said that good practice is to set the channel as far away from factory default as possible!
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And
to the forum, by the way.