Battery dies after startup what could it be? Altenator checks fine

Sounds like you solved part of the problem by running a lead from the alternator output to the battery, and since you are seeing nearly 14 volts at the battery terminals with the engine running, that indicates the alternator is working. One thing to be sure of is that you are measureing the battery voltage directly on the battery terminal posts, if you can. If there is corrosion on the surfaces of the battery posts to the cable clamp, you will has a possible high resistance between the battery and the alternator for charging, and between the battery and the loads supplied by it (especially the starter). The more current is drawn by the load, the more voltage drop (loss) you can have across a corroded connection. Make sure all of your battery connections are clean and tight. Clean them with some baking soda and water solution, just be sure none gets into the battery cells through the vent holes if it is not a fully sealed battery.

If you are starting the car when cold with a fresh battery and then start having trouble the next day or later, you are most likely losing voltage through a load that is on all the time and causing a continuous drain on the battery even when parked and shut off. I've had problems with sunvisor vanity lights staying in due to stuck switches in the visors, another likely suspect is a glove box lamp.

To find a drain that is present with the engine off, get a multimeter that can measure DC current (Harbor Frieight even gives multimeters away every once in a while as a promo), and with the engine and all lights, etc off, disconnect the positive lead(s) from the battery and connect the meter, set on the highest DC current range you can (some meters have scales as high as 20 amps), between the battery and the removed positive battery lead(s). If you don't see a reading, keep lowering the current range of the meter until you see a reading. You will likely see some draw on the order of less than 100 milliamps from things like the radio memory, and things like the digital clock. If you see anything more that about 250 milliamps, start pulling and then reinserting fuses in the fuse panel to try to localize which circuit is causing the drain, after you localize it to a circuit, then try to operate things powered on that circuit, like glove box lights. You will eventually find the cause, if you think this is too complex for you, find someone who is electrically inclined to do this for you, it will get real expensive having it done at a shop, many shops are not that good at electrical troubleshooting either. Auto Zone has excellent on line tech support reference wiring diagrams available to help you follow the mazes of wiring.