Sounds like you have a form of the DRE(Disk Read Error) it happens to everybody at one point or another. I found an awesome tutorial on how to repair your PS2 yourself. I did it earlire and now mine works like new! I was having the exact same problems you were except I was not able to play PSOne games but able to play PS2 games, lol.

Go here and read this tutorial.

http://arstechnica.com/articles/paedia/hardware/ps2.ars

::Note:: If you don't have a TINY Phillips head screw driver I found that a normal Steak knife works just as good.. lol. This tutorial took me a little over an hour to complete, this includes opening the PS2 case, taking out all the screws and removing the cover from the CD drive and cleaning the eye very carefully and re-adjusting the eye to the Default position(This is what fixes it).