Agreed, the type of detectors that were around when the Rascal was produced would be prone to sunspots with no white light filter. The Bellbox may also be a problem on hot days polycarb was much thinner and expands when it gets hot causing tampers faults.
If the panel powered up okay on mains first I would say the battery although it may be showing the correct voltage is probably fecked (Technical term for no good)as its drawing more current than the PSU can supply. Assuming that the wiring was installed well, that would be the only thing I would look to be saving from your system. If not, well.... wireless systems are pretty good nowadays.