I have been trying to figure out what the problem with my vehicle is for the last few days. I went out to eat with my friends at Perkins, my vehicle started just fine. Upon leaving my vehicle would not start. I got someone to come out and give me a jump because those where the symptoms i saw. It didn't work. Any time I try to start the vehicle I lose all power to everything, and it doesn't come back for a few minutes. I turn the key I hear the click then nothing. Before starting all of my lights, windows, heater, etc work. I don't think it is my starter because my power wouldn't go out like that. I brought the battery back to walmart (which is brand new as of Jan. BTW). Was going to trade it for a new one that I knew was charged, the lady used her little test machine thing and said the battery looked fine so they wouldn't let me exchange it. She said I could run it through the big machine that tests every single individual cell, but it would of taken 45 minutes and I had to get to work. I have heard that bad batteries can output a perfect 12 volts then when you try to start they drop to almost 0, meaning you have a bad cell. The alternator is also brand new.

I'm not a car people, nor can I give you any advice, but I'd just like to mention that I had almost the exact same problem a few months ago. I woke up one morning to drive the car, turned the key and the motor and all the lights inside turned on... and then it just died. Whenever I tried to restart the car the lights would be even weaker until it wouldn't work at all. The engine made an almost dying sound. First I thought it was the battery and I even went and bought a new one, but the problem persisted. Then I brought it to a car mechanic, and a few days later they told me that they gave it some testing and came to the conclusion that nothing was wrong with it. They gave me the car back for free, and I've never had any problems with it since.

It'd be cool if anyone here has any theory as to what could've been wrong with my car back then as well, since it's been a mystery to me. Maybe it's a similar problem to the one OP is experiencing?

Swap in a known good battery. Batteries can have the voltage you need to run lights and stuff, but puke when you try to use the starter (the biggest drain on the battery). Also, check the cables to make sure there is no corrosion (use a mixture of baking soda and water and an old toothbrush to clean the terminals and cables if needed)

Do get your Alternator checked out to make sure it is providing a charge to the battery, as the battery may be low on charge. Doubtful, but be sure.

As a side note, never let a battery discharge completely and store it that way, it will eat itself up. Use a trickle charger if the car is going to sit for a while (today that means two or three weeks or longer)

What kind of car is it...?

Could be anything from a bad rotor to a blown fuse.

Sounds like alternator to me if not the battery.

More info:

When you 'hear the click', it could be a starter relay inside the car or under the hood somewhere, or it could be the starter solenoid trying to engage the pinion, which would be louder and sound more like it comes from under the car. Which? (note: sometimes the starter relay is built into the starter motor so this question may be misleading)

If you don't have an automatic transmission, will it pop start? If so does it run good once it does?

Theory:

When you try to start it the problem is draining the battery so hard that it has to recover before it can run accessories. My guess is starter. A frozen starter or shorted solenoid will put such a draw on the battery that everything else goes dark...and it won't start under a jump.

If it has been on it's way out for a while it would explain why you needed a new battery and alternator so recently.

Test: Disconnect battery cables and remove starter (generally two bolts and disconnect some wiring, but some cars there is stuff in the way) and take it in for a test (Auto Zone, etc). If it is blocked in by exhaust manifold or other issues, see if you can undo the bolts and just back it out an inch or so. If so you can make sure the cable connected to the starter isn't grounding on anything, reconnect the battery, and turn the key (briefly). Starter pinion should shift (click noise) and motor should make whirring noise as it runs (emphasis, BRIEFLY...running it with no load isn't good for it). If you get the same result of dimming lights and such with the starter disengaged it is definitely the problem. (NOTE: if you test in place make sure you disconnect the battery again before you put the starter back in if it's good or go forward with getting it all the way out if it's bad)

One of two things. Bad battery, which most any autoparts store can Load test. that will tell the tale.

Bad ground somewhere. (this I think is most likely, as it matches your symptoms perfectly.) Check the negative battery cable. Both ends. Make sure the connection is good, clean, and tight. Make sure the cable is clamped/crimped into the ends good.

starting your car puts a tremendous load on the electrical system. Somewhere in the neighborhood of 200 amps. WAY more than any six other systems on the car combined. (unless you have a KILLER stereo. 2400 Watts or more.....)

If it does it again, wiggle the battery connectors, and see if power doesn't come back.

Someone suggested that it could be a bad solenoid.

Unlikely. If the solenoid were bad, either nothing at all would happen, or, the starter motor would run, but not turn over the engine. (makes a nice whirring sound)

Check your battery cables. That is the FIRST place I would look. (and also, the main power lead going TO the starter motor) I have been doing this a long time. Trust me.

Solenoid can be shorted (something inside shorts the coil to the case) which will give the same symptoms as having the cable shorted outside the solenoid. If the solenoid is "bad", which presumably means burned open, then nothing will happen or the motor will run without engaging.

Checking battery cables is a really good first place to look, but since the OP has already had the battery in and out I was guessing that had already been effectively done. If they were loose before they shouldn't be now. Far ends should be checked though...at the starter motor and wherever the negative cable is attached.