A blue screen can be caused by many things. Google search (or yahoo search or whatever search you use) "Blue Screen of death" and see what comes up for answers.
32 bit Windows will use only about 3.5 Gb of the 4Gb ram. it will not use all of it, because of the way it is designed.
But, when it needs more memory, your computer will use what is called Virtual memory, which is using part of your hard drive for memory, but it isn't as fast as regular ram.
I would first find out what is causing the blue screen. And then, if you figure it out, go from there.
Window 64 bit will handle over 4 Gb easily, but it could be a hassle to install it. You would have to remove windows 32 bit and replace it with 64 bit, which is not an easy thing to do. You could lose files and other things in the process, unless you back them up first, and save them. If you do switch to Windows 7 64 bit, make sure your devices are also able to use 64 bit. Like your printer, it might be 32 bit and not work with 64 bit.
So get someone who knows how to install it if you decide you want it.
But first, find out what is causing the blue screen of death.