I had the same problem, heres what I did...
OK, my PS2 was doing the exact same thing. Every time I would try to play a game it would read "disc read error." Like you, I had to reset it about 20 times b4 it started to work......Dont ask me why but my lil' bro said that if you turn the PS2 on its side, it wont have trouble reading the games n shit......Well, lo and behold I turned the PS2 on its side, and then put in a game, and I have not seen the "disc read error" message since then......So instead of setting your station flat like its sposed to be, try turning it on its side and then put in the game and see if that works.