One final note, this project seems like a really uneconomical use of time and money.
Car batteries, or if you want to go even cheaper, the "lawn and garden" riding mower batteries from Walmart, are not made for repeated deep discharge, as some other alarmist posts in this thread have pointed out. However, you start your car several times a day, but the power goes out much less frequently, and every power outage doesn't run it all the way down (if so, the UPS isn't helping much).
A few additional points:
1) The wires that attach to the battery should be big. Canabalized lamp cord or such will not work; worse, it will appear to work, until the compture runs off the battery for an extended amount of time, and then it can get hot enough that the plastic gets bubbly and then bursts into flame. (Not my personal experience, I use super heavy wire from old well pump wiring, that is about the size of the leads to a starter motor on a car -- about 12 or 4 gauge).
2) If a cheap UPS says it will keep the computer up for 15 min, it is likely not cooled enugh to run continously for hours without burning out. Look at refurbished computer places, or Goodwill Computer Works in Austin, and get the APC brand UPSs or similar, and look for those that have fan to actively cool them when they run on battery.
3) For reasons 1) and 2) above, TEST THE THING outdoors, giving it a full change and then putting several 100 watt lamps on it and letting it run down.
4) I put the entire thing in one fo those big plastic tubs, that looks like a big tuperware container, to keep acid from the non-sealed battery from ever getting on the floor. I leave the lid on loosely, so the power cords can get in and so hydrogen gas can not accumulate.
Another thing, is you can put jumper cable style clamps on the battery wires of the UPS, not close it up, and use it to make AC current for running saws and such where there is no electricity. If you do this wtih cheap UPSs from garage sales, you will swiftly find that you can light the cheap brands on fire, and that APC rocks.
A battery that may not be good enough to start your car on cold mornings may keep your computer up through occasional 3 min outages for several years.
If anything, by using larger batteries for the same length of outage that you'd use small ones for, the batteries wouldn't be run down as far. That means while charging that they wouldn't draw as much current initially (although they'd draw it for longer), which might make them easier for the UPS to charge.
What I'd imagine you might want to do is charge the batteries initially with a fast/slow charger, and then hook them up to the UPS to keep them topped off.
I don't know about the marine batteries he's using. I expect they're still designed for high current output, which is a needless cost.
You will probably be better-served to find a local supplier that specializes in battery supply, not an auto parts warehouse or a costco. Big lead-acids can be pretty cheap, if you don't buy them from UPS vendors.
Secondly, don't use a consumer piece of trash as your "scrap" unit. Large, commercial-grade UPSes are cheap as dirt on eBay, because their batteries are invariably shot. Just persuade the seller not to mail you the batteries and shipping becomes reasonable.
Marine batteries work well in this application. I've been using them for years.
The important bit in my comment is unfortunately in the second part: Don't use consumer trash when you can get the really good equipment for cheap.
Marine batteries are fine for this use. A typical marine battery might be good for 350 cycles. That should be more than enough for a UPS. (It isn't clear from the battery literature what they consider a "complete cycle", it seems like a high number for a full discharge, but even if overstated it is still plenty for a UPS).
Marine batteries do have a higher cost per stored energy compared to deep cycle batteries. I don't know if that is from the higher available discharge rate or having the word "marine" in front of them.
Renewable energy folks shun marine batteries because the real deep cycle batteries are good for 3000+ cycles, but you just don't need that for a UPS.
Real deep-cycle batteries would be better, but they're more expensive. Something like this http://www.usbattery.com/usb_solar_p1.html would probably be optimal; it's designed for use in alternative energy systems where you charge during the day from solar cells and then discharge during the night. Very heavy plates.
A cheaper alternative, which I've seen some people use in UPS systems, are wheelchair or golf cart batteries. Both of them are true deep-cycle designs, made for sustained loads.