This winter I installed a new alternator and battery on my mustang. It would start and run just fine. Took it out for a drive the first time the other day and it would almost die going over bumps. Then on my way back home it died on me. The car turns over but doesn't start until battery is charged above 12 volts. I tested the battery while car was running and it ran a little below 12 volts. I don't understand why its doing this because it has a brand new alternator and battery. I lost my keys a few weeks ago and had to get a new ignition lock cylinder but I messed up the housing so bad I had to just get a whole new column with the key. Could there be an issue with that? Or am I dealing with something else?
Pull the alternator and battery, have it tested at the place you bought it from. Or better still, if the car is drivable, take it to the auto parts store and have them check the charging system. They will do it for free in most cases.
Some replacement alternators have high DOA rates and often fail shortly after they are put into service.
A poorly performing battery will often cause the alternator to fail, and will not supply enough initial voltage to get the alternator working correctly.
I had same issue and found that the grounds up near the battery under the green screws were the culprit on an SN95. The 92 I have does not use them but has another ground on the chassis for the same purpose. You can remove the hold down screw and sand the metal frame and then bottom of the ring connector to assure you have a good contact and see if that helps.