We have had all three types and all the various probes.
The AM503 503A and 503B are very different and TEK never released a AM503B service to my knowledge.
The backup batter should be easy to find an replace.
Cal may require more details. Rico's note link?
If the probes have no DC response it is a failed or damaged Hall effect in the clamp and you see only the AC signal.
The probes are typically impossible to fix. The adjustmens may also be inside the probe case and not all exposed.
If the probe was off epay and seller said it was good, it probably is not and should be returned.
Bon chance,
Jon
Jean-Paul