Right clicking "Computer" in Explorer, choose Manage, then Device Manager, then Display Adapters, and it'll show you what you have. You will see everything Windows has registered. If you can't see GT 630 there, then it's not installed. It may be physically installed, but drivers are not... not always that simple. It should, however, be visible even without drivers, then it should have a yellow question mark, perhaps like "Unknown device", or something.
You can also get info with CPU-Z,
http://www.cpuid.com/softwares/cpu-z.html It's free, it's light, and reliable.
Windows Experience Index doesn't affect anything, it's only an indicator, it doesn't control the computer. The main thing is that games run, which apparently is not the case.
It may be, that in BIOS you have the onboard video card set as default. You should change that. The command to get to BIOS varies according to motherboard. The safest way is to check with the manufacturer. And DO be careful with BIOS, if you get there. You may mess everything!
All for now. Best wishes.