Actually your PS2 won't play CD-ROMS (Some PS2 Games are on CD's there have blue bottoms) this is actually a common problem that happens because the laser for your CD-Rom reader has been knocked out of alignment. Any Gold bottom PS2 game should still work. You should contact sony to see if they still offer free repairs.
There is a rumored problem with PS2s that if you play DVDs on them it burns up the electric motor in the drive faster. Your PS2 is over 2 years old.... DVD's spin at a much lower RPM than games.
you most likely have a wrong region code games. there's europe region games and north america region games. If ALL of your games doesn't work, you obviously have a broken PS2. try cleaning the lenses before.
This is a problem with the voltage of the laser. If you have some electronics knowledge and a multimeter, you could adjust it yourself; a professional would be better.