61x will tow start, but you wont have lites if battery is dead. If the battery is dead after a drive in, something is using current beyond the ability of alternator to generate it.

An old battery may not hold or take a charge. Check the fluid level, top off w/ distilled, or at least bottled water. (Put on safety glasses, pop the plastic caps off w/ screwdriver. You should see 6 or so total holes, each w/ fluid level about 1/2" from the top. Top off, replace caps, seat them w/ handle of screwdriver). Have it charged & load checked for free at autozone.

Your other battery, if good, will hold a charge for several days. Keep it in the trunk to replace, not jump a flat battery (less than 12 -1/4 volts or so). Charge it up every few days until you are at 'problem solved'.

Parts store like autozone will charge & load check battery, tell you if it's good. They may check the following things for you if you ask nice. Write them down as you go:

Battery voltage.(VOLTS) -Should be 12.6+ after sitting overnight
Charging voltage at idle, when revved. -should be 13-15 volts.
Current flowing from battery(AMPS):
When keys are not in ignition, all lites & accessories off -Should be nothing.
Ignition at run, all lites & accesories off (wait for the glow plugs to stop) -Should still be nothing.

If the battery is very low, it may not energize the battery enough to charge.

Are you near a harbor freight? $3.99 will buy a decent multimeter, $7.98 will buy two so you won't be sad or angry when one dies. A deal at twice the price. A useful multimeter is still worth almost any asking price when you need it, so get one and learn to use it. They come with instructions of varying quality. Haynes, Chilton and mercedes benz manuals for the W123 cars all come with basic electrical troubleshooting instructions. Looks like you either have a current leak (short circuit), a bad charging system, or both. A short circuit can light off your dashboard if it's hiding there, and the rest will follow (ask the guy with an engine sitting in a smudge mark).

Report back if you get any information.