The first thing I would check is whether there is either a dedicated ground wire going from the engine to a ground point on the firewall; or two ground wires coming from the negative battery terminal; the larger one going to an engine bolt, and the second wire going to a body bolt. The battery MUST be grounded to BOTH the engine and the body. But the factory ground wires may have been removed or damaged during 12 years of service.
If the auxiliary grounds are intact, an additional possibility is that one or more alternator diodes have
gone bad. If this happens; the alternator may still produce enough
power to keep the battery charged, but the alternator output waveform
will be so uneven that it adversely affects the computer and ignition
system. Depending on the quantity and location of bad diodes, a
volt/ohmmeter will not always detect this kind of problem. For that reason,
an oscilloscope is sometimes the only tool that can be depended on to
find bad alternator diodes. Of course, it is also possible to substitute a known good alternator.
I would also consider the likelihood that the rebuilt computer has a fault in it. Many specialists refuse to use rebuilt electronic components; because of the likelihood that the testing of those components was insufficient to cover all the possible issues which could occur. For that reason, I would prefer to get a used OEM computer from a wrecking yard, rather than a rebuilt unit.
I hope this helps!!!