I bought a slim PS2 when it came out, but I got an original "fat" one in 2002. I was digging through my garage and found it on a shelf, where it's been accumulating dust for, well, some time now. I blew on the fan and some of the intakes to get rid of some of the dust, but I think some of the dust went inside the console. Could that cause problems in the future or will that dust just get ejected by the fan? Also, could dust in the empty controller ports and memory card ports cause damage? Or will one of those aerosol dust removers fix that?

my it's all dusty. its a ps2 fat from 2003.
but still works =).
but yeah dust inside can cause problems

I'm not recommending that you do it, but I've opened up my PS2's several time. Once, I fixed the dreaded "Disc Read Error". It's fairly simple. If anything, get a can of compressed air, blow it out, and hope that nothing in that garage (weather conditions, fumes) caused any corrosion inside the PS2. Good luck, and godspeed.

Just see if it works first.