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.