Alero needs a jump!

I have a 2000 alero. This is not a pass lock issue, been through that before. Battery has 12 volts sitting alone, not running. Ample supply of power to everything that I can seeCar will not turn over without a jump from another source. No loose or frayed wires on alternator, battery, or starter. Started turn over fine with a jump to battery, and alternator puts out 14 volts , but vehicle runs like crap at 3/4 throttle driving or parked. The motor revs up fine, then drops power and quickly gets back up again over and over. Idles fine, and no codes stored in computer, I checked. Help!

I had a brand new battery here, tried it in there and things seem better. I guess with the De-frost/Air Conditioner on and stereo and lights it stressed the alternator to the point of cutting out on the ignition or fuel pump, not sure which. Only misses at 4000 RPM in park, I guess the Alero's have a rev limiter in park , who knew? Over the years I have done window motors, key ignition(Security Pass Lock problem) brakes 3 time, and hubs. This was the first to ever stump me, and something so simple. Guess the Alero has a favorite Volt to run in.

Just FYI-- just because a battery has 12 volts sitting static, doesn't mean it has enough power to support the amperage draw required for starting. The starter motor generally requires anywhere from 100 to 300 amps to get it going and keep it running depending on engine and starter size and health. You can turn on a lot of lights, radios, etc. with the car not running and never come close to that kind of amp draw, so this doesn't necessarily provide a good indication of battery health.