Hopefully Joe is right and it is just sloppy/low system voltage that is creating problems for the computers. All the various computers (PCM, TCM, ABS control module, Air bag sontrol module, ATC head, etc.) communicate over the PCI bus. Hopefully you can get it all working by replacing the battery. If not, somethings shorting out the single-wire PCI bus.
Besides battery, it could be poor power system connection, so check for corrosion and poor connections at the battery posts and at the two jump posts.
How old is the battery?