How important is buy and play to you v. saving a few bucks? How important is having a trackball v. that layout? How quickly do you need a cabinet v. getting a good deal?
You shouldn't pay anything for a PC to play Mame. Any P4 and above is going to run almost everything without issues. You can easily find a P4 or higher for nothing or next to nothing on Craigslist, Freecycle, Goodwill etc. You can pick up a 25" or 27" crt television pretty cheaply or for free too. Depending on what controls you want (trackball, encoder, joys and buttons for two people, you are looking at $125 to $150 (ballpark). Find a empty cab and offer to haul it away or pay $25.
If you're frugal and take your time, $300 should get you what you want (again ballpark).
If you want to build, do you own tools? How much time do you have to work on it? Again, it comes down to convenience, cheapness, desire to play now v. build.
$800 is high. $600 is better but more than I would spend. What's the most important thing right now for you?