You should get a voltage meter and check it. That's the easiest way.
Batteries typically rest at something like 12.3something volts? It's something close to that.
But with the engine running, you should see something at least in the mid-to-high 13 volt range. If it's lower, then your alternator isn't charging - but that is not always the sign of a bad alternator. It could also be the voltage regulator or wiring.

You can get an electronic multi-meter pretty darned cheap, and they are very handy to have, if you work on anything which uses any electricity.

 

Definitely get a meter! It'll tell you many things...

But yours does sound interesting. New battery lasted a full week without draining, but after one drive was dead? Usually something wrong with the charging system.
But jump it and it ran just fine? For how long? If it kept running for an extended period with just a quick jump, then likely the alternator is charging. The vehicle basically runs on the alternator when the engine is running, and on the battery only when it's not running, or the alternator not charging.

It's possible for a bad battery to just go dead all on it's own, and a new-ish battery can go bad too. But that doesn't sound like what's going on here.
An alternator can drain a battery quick when the diodes are failing. Usually it's a quick drain, as in, a couple of hours. Overnight for sure. It doesn't always do that, but often enough it's a quick drain.
A bad voltage regulator can drain the battery too, anywhere from a few hours to overnight as well.

You should get the meter to be sure, but when a battery is dying consistently overnight, in a pinch you can disconnect the battery negative cable to see if the battery is still dead in the morning. If so, it's your battery.
If it's still good, then it's something draining or not charging.

With your new meter (Harbor Freight gives them away free with a small purchase) you should see hopefully between 14v and 14.7v at the battery terminals when the engine is running. As meangreen said, if it's 13 or less, it's just not enough to keep the battery charged.
MG and others can run down any other testing procedures that might come in handy here, but those are some bits of knowledge you can start with.

Good luck.

Paul

 

Cheap and quick test, disconnect your negative cable from the battery. Clip your test light to the cable, then touch the tip to the negative post. If the light lights up, you have a drain somewhere in your system. You really don't even need a test light, you can improvise using a spare light bulb. If it does light, start pulling fuses one at a time - when the light goes out, you have found the guilty circuit.

 

Do you have an aftermarket stereo/amp wired hot? DO NOT START IT AND TAKE DISCONNECT THE BATTERY CABLE TO SEE IT THE ALT IS WORKING. THAT IS A GREAT WAY TO FRY AN ALTERNATOR.

Take the alternator off and get a ride to the parts store or get a jump start, drive to the parts store and in the parking lot take the alternator off and get it bench tested. While you are there get a cheap multi-metor, they even have one with a battery ck setting. After they tell you the alt tests good...like always.... put it on, start truck or get jump start and test the battery (while the truck is running) with the new multi-metor to see if the battery is taking a charge. Yes it should fluctuate around 12... ish to 13 to maybe 14 ish and back down.

Results point to a bad alternator or a voltage regulator. FYI (77 to 79 inner fenderwell passenger side, 1 blade plug) 73-to 76? its on the passenger side, back side of the radiator core support. FYI cheapest is NOT the best route on that part.

 

Had a trunk light on a car killing the battery because I parked on a incline. You don't have a glove compartment lamp on do you? Very few systems have power on a dent with the key off. All that I can think of are lamps. except alt and voltage regulator.

 

Even with a lamp or with an aftermarket stereo I can't imagine something that would drain a battery that fast. It sounds like his drain is HUGE....definitely sounds like a recharging problem

 

Mine had a hot restart issue that looked like a bad battery. Cleaned up all of the connections which made it much better.

The test light trick works great. Especially if you remember to close the door so the dome light isn't on.

Michael

 

You'll likely have to check the entire electrical system, but do remember that batteries can have internal shorts or "opens" which can be intermittent.