PS2 does not work like a PC. The graphics chip is almost "dumb".
Most graphics stuff are calculated/processed on the CPU.
And these problems are usually caused by two things:
Poor connection from the CPU (Emotion Engine) to the Graphics chip (Graphics Synthesizer)
RAM problems on the CPU.
The PS2 RAM chips are of a special type that is only used on PS2 consoles so it might be difficult to find chips you could use to repair your unit. I suggest you go find a new PS2 instead...
SCPH-10000_GH-001 SCPH-15000_GH-003 SCPH-18000_GH-008 SCPH-30001_GH-005 SCPH-30000_GH-016(V4) SCPH-30001_GH-010(V4)
2xSCPH-10190, 2xSCPH-10350, 2xSCPH-10280
"**** j0 hackers!"
-Sjeep (As seen on TOXIC OS ELF...)