Mine started giving me trouble with 6 months. Don't rely on age when it comes to electric components...

A complete cleaning shouldn't be too expensive, just send it to a specialized store you trust (or else they'll steal some components - personal advice). It shouldn't cost more than $30. Honestly, I paid even less, and my console came back as new after a week (I had to buy a new board or something like that, so it took longer than expected). Two to three days and it's back. Don't worry too much about it, though; if the rest of your games start giving you trouble (even the non-scratched ones), then, start to consider a cleaning, because once a PS2 is open, it will never be the same again...