These problems are common occurrences in my home network which is using the Linksys WRT54G model router. I've had this for quite awhile, but it's always worked to my satisfaction.
I've been noticing quite a few times where I will get disconnected from the internet (on WiFi) and a quick reset of the router will usually fix this problem. I'm assuming the problem lies somewhere in the router itself, but I don't have a very suitable base of knowledge on networking to verify this assumption. Another, probably unrelated, problem I have commonly is when my PS3 powers on I lose internet connection on all devices in the house. The PS3 is connected by ethernet cable. I'm not sure if other wired connections are affected by this, but I do know all wireless connections are affected by this.
I had a similar issue with a dropping connection in the past. Power cycling the router does work, for a while, but i eventually got a permanent fix by changing my DNS service in my router.
Amongst Cablevisions many undesirable qualities, is a flaky DNS server that blinks out occasionally. after this, the modem would come back up, but the router would need to be power cycled to see regain network connectivity.
I changed my DNS server to OpenDNS (instructions on their site) and i had not had a problem since.
The PS3 issue, sounds like a network card issue on the PS3. If a device powering on (or off) effects other devices, then a faulty network card is pulling everything down.