If you were a skilled eletrical engineer, then such a thing might be possible, but for the average person, not a chance.
Most automotive batteries are very low voltage (car batteries tend to be ~12V DC) with very high amperage. You'd have to do some reasonably complex wiring to convert that to 120V AC, and also step down the amperage. Along the way, you'd lose some energy in the conversion process, since that's just how the physics work out. Then there's all sorts of potential fire hazards to be considered if any of your wiring is faulty.
In the end, even if you were able to pull it off, car batteries really don't hold as much power as you think. They send a low power, high force, charge to the spark plugs which ignights the gas and kick starts the alternator. I doubt a car battery would be as good as even a 250VA UPS.
What I'd do, is probably take out the batteries of the old UPS units and dispose of them properly. Then just make use of the surge protection features offered in almost every UPS, which should work without the battery. Use those for less important things, like your TV and stereo. Then get a new UPS for your computer. And if I might make one more suggestion, get one that has AVR (Automatic Voltage Regulation). Power supplies are one of the most common parts of a computer to fail, in part because of the normal dips and surges in the power feed. AVR will smooth that into a nice steady sine wave which will extend the life of your power supply, and thus your computer. Such units often cost a bit more, but when you factor in the cost of a new power supply, even a cheap one, it usually amounts to more than what you paid for the AVR feature.
I have 3 "older" UPS units that were originally bought and used for Pentium 1 computers and my home stereo system. Batteries for these units have finally "bit the dust" or at least don't seem to hold a charge. This seems to be a known "dated obsolecence" problem with most home user (lower end) UPS units. One unit is a Tripplite BP600 Pro (which at the time was enough to handle all my needs), another is an APC 600, and the third is a small APC 280. All three have the same problem-batteries just don't hold a charge. Specified replacement batteries just seem to cost more or equal to new 1000va units and/or are not readily available. Does anyone know if you could replace these "small batteries" with larger batteries say a small car, cycle, or tractor battery(maintenance free of course)to get a little longer life? Since the cost and availability of these batteries is much better, I think the overall investment would payout better. We are running Pentium 3-350, 733, and a new tower Pentium 4 3.0 ghz; 300 watt, 350 watt, and 600 watt power supplies-respectfully.
Any response would be appreciated.