My v1.0 WRT54G died the same way only about 2 months ago. I was browsing the web fine, when suddenly I lost the Wireless. I went to reboot the modem and router, when I realized the Diag light was solid. I did the reset (Hold reset button on back in for about 30 secs) with no success about 3 times, then gave up and bought a WRT54GL, and haven't had a shadow of a problem since. A word of advice for when you get a new one, is if you go Linksys again, go for the WRT54GL as the lates WRT54G (v5.0) has been cut down a fair bit commpared to the GL in terms of its flash memory and other bits and pieces. The GL will also allow you to use third party firmware if you wish. Personally I don't, but the option is always there.
When I got the GL setup (Took under 10 mins, thank God. I had a lot of work to catch up on!) I put the v1.0 aside to play with later. I found a guide online of how to "De-brick" the WRT series (Bare in mind it involves taking the system apart, voiding any warranty you may have.) and gave it a shot. Sadly, it didn't work which lead me to think that a hardware failure had occurred. I have read that this is common on v1.0s, so I guess we're just amongst the unlucky ones!
Hope this helps,