Although you've tried cleaning (I'm assuming a lens cleaner disc), if you're handy with a screwdriver it might be worth a look in anyway - lens cleaners don't always get everything.
I got a Playstation 2 years ago from an old workmate with the same symptoms - he thought the whole unit was kaput and bought a new one, so I asked for the old one. Had it apart in 5 minutes, and found a huge great bloody piece of grit inside...cleaned out and it worked no problem after that.
The other thing to check before you condemn it is dry joints / loose connections - a dry solder joint will appear a dull, matt grey instead of the usual shiny silver, and plug / socket joints can fail over time.