it sounds as thought the battery has not been getting cycled too much of late (with the rebuild and all). again, really charge it. they can show good volts, but if not charged or defective, they dont have amperage to turn the car over,etc.
might be easiest for you to take it to the parts store and ask them to check the charging system out. takes a minute and is normally free. you can check each component, but it may be more involved than you want to get. it is always a good idea to check the components they suggest as bad for yourself. and have them bench and load tested when you take them in.
if you get a new battery or alternator, have it load tested before you buy it. they can often be bad off the shelf. if it's the alternator, might be a good time to do a 3G upgrade. will help with just the problems you have.
were i you, i would take it to the store for a check out. also clean the battery terminals. are you sure all the ground wires were reinstalled? the ground situation is already marginal, but leave one off, and you can run into problems. insufficient ground, and everything suffers. just my two cents worth.
good luck.