32 bits? Still, depends on the OS ... you can play with around 1300m to 1500m on windows, some people have reported success with 1990m but failure at 2000m.
Or are you running out of PermGen while loading?
There is no easy way to tell which mod is using how much memory.
What you can easily do is toss more memory at minecraft.
So what is the physical memory of the computer?