You're sure having some bad videogame luck.
There's no obvious scratches on the disc? That's just so weird - even if it can't be read, you should get a screen saying it can't read the disc - not just a black screen.
But... I did a google search and found this not-so-encouraging news:
PS2 will not read or recognize the God of War disc (DRE)
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This isn't a glitch with the game, but a problem with the older PS2 hardware.
If the disc is new or if cleaning/resurfacing the disc does not help, then
it may be a DRE (Disc Read Error) that some of the older PS2s have. If you
get an error on screen that says "Disc Read Error" when you try to power up
God of War, then you've got the DRE problem.
The problem is with the PS2 laser itself. It has either slipped out of proper
height alignment thus throwing off laser focus, or the laser has diminished
in overall amplitude thus diminishing its ability to focus. This is a slow
process of PS2 hardware degradation in which the PS2 may still read some discs,
but will have a problem reading others. Since God of War is a dual layered
disc, an older PS2 with a DRE problem will likely have a problem reading the
disc.
The only way to fix this problem is to adjust/repair the hardware (the PS2).
More often than not, all that is required is a simple adjustment (turn a
screw a few notches) in order to get the laser back into position for proper
focusing. In some cases, however, the laser itself needs to be replaced.
Sony fixes DRE problems on the older PS2 models for free, but you have to pay
shipping and handling. There are SEVERAL web sites on the net dedicated to
DREs and how to fix them yourself if you're technically inclined and feeling
adventurous.
Basically, if you get a DRE, then you'll have to put the PS2 in the shop or
buy a new one. The newer PS2 models have added protection and more robust
laser systems that help avoid this problem.
http://www.gamerhelp.com/ps2/GodofWar/107204.shtml