If it only has a VGA port on the back then you cant use digital video out. You cannot go from analog to digital with an adapter cable, DVI-VGA adapters trigger the integrated Digital-Analog converter, but there is no Analog-digital converter to go from VGA to DVI, so unless you have a DVI or HDMI output you are restricted to VGA monitors.
The idea of a VGA to HDMI cable is completely worthless. The crazy thing is companies actually sell them, but it really is basically a scam. VGA is an analog signal and HDMI is digital. A cable isn't going to perform an analog to digital signal conversion, so it just isn't going to work. In fact I recently found this website that talks about that very cable and what you can actually use to do what you're suggesting. Check out the really helpful VGA to HDMI Cable explanation.
Hopefully that'll really help clear things up and save you from wasting money on a VGA to HDMI cable that won't do anything for you. It wouldn't even make a good paper weight.