The wiring harness on 240s produced before the '88 model year were prone to crumbling insulation, which caused any number of electrical problems. If you have only had the car for 5 years, it may have been replaced already. If you have no other electrical gremlins, disregard that for now.

Regardless of how old the battery was, the fact that you just replaced it suggests that your charging system may not be up to snuff. The symptoms you describe - the car "petered out" - sounds like a low charge on your battery. If a month old battery has a low charge, you either have something drawing constant power when the car is off, or your alternator is not putting out enough voltage.

How did you try to charge the battery? You should buy or borrow a voltmeter to test the battery voltage, then the charging voltage while the car is running (if you can get it running).

Have you tried jump starting the car?

If the alternator is not charging the battery, it could simply be that it needs new brushes, which may be as cheap as $10.

Your first step should be to verify the state of the battery beyond just trusting that it is good because it is new. If you have another car, you might try simply swapping batteries to see if your 240 will start. That should immediately tell you if the battery is the problem.