First I would uninstall PCSX2 and then reinstall since this seems to be a copy of it from your laptop. Start Fresh. You can save your memcards from the memcards directory. If you have save states, same them from the sstates directory. If you have sstates make sure to install the same version of PCSX2 or else they won't be compatible. If you don't have states, I suggest downloading the newest SVN from here(memcards will still be compatible):
http://buildbot.orphis.net/pcsx2/
Also, don't forget to back up your bios!
After that:
It looks like a bad shadow effect.
Try this:
Config -> Graphics -> Plugin Settings
Tick Enable HW hacks
Click configure by that
First try the alpha one. Test. If not better turn it off. Then try alpha stencil. Test. If not better turn it off.
Make sure all are off, then set skipdraw to 1. Try again. Keep increasing by 1 and trying. If you get lucky, one of them will disable that
BTW with your rig, in the GS settings you can set some multiple of PS2 resolution if you want. 2x, 4x, 6x, etc. It will make the game much higher resolution. But don't do this until you fix this issue. You might know this, I'm just saying it in case you don't.
Show me a screenshot of spiderman 2, please.