If you want to connect your PC via VGA to your TV and get full 1080p resolution, then you can use VGA-HDMI adapters which lets you essentially plug your PC into the HDMI port on your TV.
However, these adapters are hard to come by and the success of them varies depending on the TV and other factors.
Your best bet would be to get yourself a DVI-capable graphics card for your PC, which outputs a signal via digital DVI rather than the old analogue VGA.
Most new graphics cards have these and can be bought for quite cheap (you would also need a DVI lead to connect to your PCs monitor).
Then you should buy a DVI-HDMI adapter, this is like the one I mentioned earlier but cheaper, more available, reliable and better quality.
Buying a DVI graphics card and the HDMI adapter for it lets you plug your PC into your TV like you would any other HDMI equipment, and gives you full HD 1080p picture quality. There is also the added benefit that when you plug the DVI card into your PC monitor (I assume you'd switch between TV and PC monitor) you get a better picture quality than you currently have with VGA.
Just ensure that your current PC monitor supports DVI - it will have a white (I think it's white, mine's white) socket near to the VGA slot.
I've explained this in as much depth as possible just in case you aren't into PCs that much - but if you are then don't be offended by my patronising tone, I just wanted to make sure!