Hi,
Sounds to me like your leisure battery is goosed.
I know you saw 12.4 V on it but that doesn't necessarily mean that it's fine.
If your lights are ok when the engine's running but fade soon after you switch off then that's very likely to be the problem. The lights will draw less current than the fridge, so if the battery isn't holding enough charge to keep them going, it won't run the fridge, either.
Depending on how efficient your fridge is, how big your battery is and how hard it's having to work to keep things cool you might expect to get a couple of days out of it before having to re-charge but there's a very wide variation in that....
Hopefully that's the only problem...
Cheers,
W.