The answer is a firm maybe.
Without opening your PS2, you can:
- Clean your DVDs
- Clean your DVD drive
- Clean the inside of your PS2
If you do open your PS2, you can also:
- Adjust the read angle of the laser
- Adjust the laser voltage
Your Disc Read Error messages might be cleared up by the first three steps. If not, you must move on to opening your PS2.
First, clean any DVD's that cause the Disc Read Error. Check them for nicks, cuts, scratches, and debris. The problem may not be your PS2 at all.
Next, blow out your PS2 with a can of compressed "air." This won't clean the inside of the PS2 as well as you could if you opened it, but it can improve cooling and reduce errors caused by dust particles.
Use something like this
Beseler DustGun 100 Compressed Air canister to do the job. Don't use a vacuum cleaner, the static electricity generated by the vacuum would likely kill your PS2.
Then, use a CD/DVD cleaning kit on your PS2's drive. Something like this
Memorex CD/DVD-Player Laser-Lens Cleaner should work nicely.
You will want to use the compressed air before the cleaning disc, because the compressed air can kick up a lot of dust.