Have to agree here your specs are pretty low and TMO has some mods to the weather and I bet that puts up more demand on a very low spec machine.You might want to try going into graphics and un checking post processes and basically reduce everything graphics wise down and turning off VSYNC.
A fact of life in the hobby of PC gaming is that you are going to have to upgrade your gear every few years to keep up and as others have said minimum specs is pretty much a gimmick they always set it too low to get more sales.But at mins a PC game is just not going/look to run very well 90% of the time.Honestly you seem to already know this but are complaining anyway.If you want the game to run well and look half way decent you are going to have to upgrade somethings and also install mods properly if you do both of those CTDs and such should be pretty rare.
This is what I have:
Q6600 2.40GHz
3 GB RAM
Vista 32 bit
8800GT 512MB
I run SH4+TMO (several other mods work fine too) @1680x1050 with graphics settings full with no issues hardly ever maybe had 2 or 3 CTDs with stock long ago.
You can buy an 8800 range card now for less than $100 and RAM is pretty cheap too.Even on a limited budget that is not to much money over time.
By the way:"I could have settled with a pirated copy,"