Define 'spending a grip'? (i've never heard that expression)
Building a bike up from parts is not usually cheap unless you are extremely patient or if you already have a decent number of spare parts in your possession.
The main benefit of building up a bike is the satisfaction of doing it, and the ability to have every part to your own specification.
The cheapest way to do it is probably to buy a new mid-range bike online, like a Motobecane, strip off the parts, and sell the frame. I haven't heard of anyone actually doing this though, but it would be cheap. For example, buy this:
http://bikesdirect.com/products/moto...rage_pro07.htm
Then transfer all the parts you can to the old frame. Seatpost, headset, stem and BB may still not work, so you may have to find replacements.
Then sell the frame on eBay for $80.