Answer:
Depends on the nature of your problem. I've had problems with both PS2 models & despite all the great games they made for it, I hate the PS2 - Sony needs to really work on making better disk drives, you don't purchase a game console, only to have it break on you for trying to use it. Very poor quality product from Sony, not like the original PS1 (PSX) model. (& they won't repair them for free or give you a new one, which makes me even more mad)
Anyway - Take some rubbing alcohol, & whatever you do? DO NOT use a DVD disc cleaner disk, the fine needles to brush the laser lens on those will SCRATCH the lens on the PS2 and damage it. Take a Q-tip or similar light fine cotton, not kleenex or towel that will also scratch the lens, then dip the tip in the alcohol and lightly clean the laser lens on the PS2. You're problem is more likely that it is dirty & dust got inside the system. Take a vacuum or better a can of air and blow out all the vents in the PS2 around the sides, both with the disk cover open & again with it closed, to either "suck" or "blow" the dust out of it. lol'z, k
attempt to repeat, either I would blow the dirt out of it first, then take the rubbing alcohol and clean the lens, apply one little drop on it & let it dry on it's own, don't blow on it with your mouth or try to dry it. Give it a few hours to dry, then fire it up. If this doesn't get it working, then it's the motor on the lens that moves it, or other damage & you need to send it for repair, or better just buy another one for cheap & forget it. Save you the headache. Hope this helps, it did me with my slimline model , same one you have.
Again, I hate Sony for doing this with all the PS2 models, all of them I've owned 3 and they all had problems.