Nononon. Don't attack something from the wrong angle. Ok so your RAM is a little low. Can you put more in? What CPU do you have? Even a basic old CPU with a decent amount of RAM (1GB or maybe 2 if supported), and a new video card. Even a basic video card will do your requirement.
If you upgrade your RAM and buy a very basic $50 video card you can probably get this all working for under $100.
If you do go with a new computer I suggest the following:
Intel Core2Duo or Core2Quad at a minimum. Don't buy those Celerons. Same go for AMD there's several classes of chips. Cheap, normal and workstation/server class. You don't want the cheap ones, as much of photo editing is very intensive on cache which is what the cheap ones are missing. As for actual GHz speed? Doesn't matter. The slowest Core2Duo is still better than a faster Celeron for photo editing.
RAM: It's cheap, don't skimp. Windows 7 will eat up 1GB just idling. You'd be mad not to put more than 2GB in. Like to edit large pictures? With Lightroom, Photoshop, and Windows 7 as the only thing running on my computer with Photoshop having a single RAW file open you will be on the very edge of 2GB already, so get 4GB if you want to try your hand at panoramas.
HDD: 1TB. It's cheap again.
Video card: As above you don't need the latest fancy Nvidia 295GTX. Even the cheapest card from the current lineup will not only run your screen just fine, feature analogue, digital, and possibly even TV connectors, but will also likely run the current generation of games reasonably.
Motherboard? Your choice.
Powersupply? Don't get suckered in to buying excessively large powersupplies. I run a top video card (which chews the most power), Core2Quad, 4xHDDs and a DVD drive from a 550W. The key is to get a quality PSU. Not a no-name. I've been happy with Antec as a brand but there are plenty others out there. Crap power is the biggest source of hardware failures.
You can build an absolute beast of a machine for under $500 these days.