If you are running Windows, go to your desktop and right click on 'My Computer', then choose 'properties' down at the bottom. This should bring up a window that will show how much RAM.
What operating system do you run now? Windows XP?, Me, 98, or are you off on the fringe with Linux?
Does your school have a recommended laptop setup on their website? Usually the school will give you guidelines as to what you need. Chances are the only program you'll have to worry about is the test software. I assume you already have Office with Word, Powerpoint, etc. Unless you plan to purchase new note-taking software this should do.
Do you have an Ethernet card to connect to the school's network? A wireless card may be recommended by the school, but from what I've heard, even the best wireless networks at schools are flaky. If you can plug into the network in class you are probably better off.
If you feel your current laptop is too far below what your school recommends, consider that a new Sony will probably run you around $2K (ballpark). This is likely a small amount compared to your school loans anyway so it might be worth it to upgrade to a new laptop (with a new warranty) and keep your current Vaio as a backup. If you feel comfortable enough leaving a laptop at your school, you could just transport your files back and forth on a USB drive and not lug the computer all around.