Try cleaning your PS2's laser before you EVER think of trading it in for mere credit on a slim PStwo. This is a video I found on YouTube which shows you step by step how to open the PS2 to clean the laser. Hope this helps.
Link:
http://www.youtube.com/watch?v=Jhof6WtePyM
If that does NOT work and your PS2 is still finnicky about which discs it'll play, you can always try laser replacement. It costs about 40-50% the price of actually buying a slim and will surely give your PS2 about another 5-7 years of play time(or more depending whether or not you use your PS2 as a cd/dvd player too).
If you're too leery of opening the PS2 up to clean it or replace the laser though, you can always call Sony and for $45 they will replace it with a refurbished model(which comes with a 90 day factory warranty I believe) or for $75 they will fix the disc read problem you're having. Thing is, tack on the cost of shipping and sending it to them may cost $60-100 total, so trying to fix it yourself is almost always the best FIRST option.
If you DO send it into them later on though and tried the cleaning first, DO NOT mention the warranty seal is busted or they will hang up on you. Their number is 1-800-345-SONY(7669) for the repair line, just follow the prompts.
However, if you're ok with messing with your own system and replacing parts, I listed a site below with usually free shipping on items that can help you out.
www.richspsxparts.com is a site I found which gives free shipping on most items AND has a compatability guide on their site to tell you WHICH laser you'll need. The hardest part of replacing the laser is probably putting the disc tray back in right after you open the PS2, but there are also YouTube videos for that I believe. Note that the laser AND controller ports are both held on their ribbon cables via a small plastic 'door' which snaps open and closed and holds the cable in place. Gently but firmly open that door to get the old laser off its ribbon cable.
WHY everyone ALWAYS suggests to plunk down $130 on a new system is beyond me, when those 2 steps alone will fix 90% of disc read problems. Almost EVERY part in the PS2 can be replaced without having to buy a whole section of the system and actually the reason some systems seem to 'die' is that the battery on the motherboard(typical watch battery used for the clock and some other functions on the system)has died.
Anyway, try that video first, then try out the discs to see if they work now. If they do, congratulations, as you just saved yourself $130. If not, then the laser is probably too weak to read those types of discs.
Do you have problems with ANY other games in your collection? If so, what kind of disc are they on? Also, do you use your PS2 as a dvd player AT ALL? That can wear down the laser a whole bunch and shorten the time before you get the almost inevitable DRE. I've listed the disc types below so you know what to look for when mentioning which games don't work.
Blue bottom-PS2 CD based
Silver bottom- PS2 DVD based
Gold bottom- PS2 DUAL LAYER DVD based
Black bottom- PS1 games
Hope this all helps.....
