Open the case if you can and read the label on the power supply and tell us what your PSU is rated at. It's very possible that the PSU will be very low and you may need to upgrade it.
Also, are you sure your motherboard has a PCI-E slot?
Thats a good monitor, and should look great if you get a new video card
I'll have to wait until I get home to check the PSU, I'm currently at work.
I do not have a PCI slot, strictly AGP.
Again my Vaio is completely stock, just like the day it was shipped. Could I find the PSU from a specs sheet?