If your BIOS clock is slipping and BIOS is losing settings, this could indicate your motherboard's battery is going flat. They usually last the lifespan of a computer though (never had to replace one) but this could be the cause. If you do decide to replace the battery then you might lose all your BIOS settings, so note them down. If you pop the old battery and get the new one in very quick this might not happen.
BIOS viruses are very rare these days, most viruses want to use your PC as a zombie so they won't try and disable it. If you're worried, you could do a BIOS update.
This wouldn't explain the wireless router problems, though a friend of mine has a Belkin and he regularly has problems with it cutting out randomly. So perhaps the two problems are unrelated.