as above

What are the readings over the battery terminals?

4.x volts

about 4.5v for battery itself, and around 14v on the charger wires. Battery is disconnected.

14 volts? Panel replacement required imo.

Does this means that the fuses have failed to do their job, or are they not protecting that part?

a fuse can only protect so much. most psu cant blow a fuse without a working battery.

fuses only work on a functioning system

yours is outside that

Sorry Gemini but everyone here is correct. Sling the panel and put a new one in. Alarm panels shouldn't be treat like regular consumer electronics where 'everything can be fixed with a multimeter and a soldering iron'.

This panel is ancient and is well overdue a replacement, more so with the lack of maintenance. You'll save yourself the chew, headache and money in the long run by replacing it.

No disrespect to you but the trade guys aren't here to tell DIYers not to do it and work you up, they're here to help you and advise you, so take their advice because there's nothing else you can do!

Believe me, I also like to prove that a product is fully gone beyond repair before I chuck it, but then again, my side hobby from IT is electrics and electronics, and has been for the past 10 years and not to sound big headed, I know what I'm doing (98% of the time )

However, if multiple experienced engineers/tradesmen (regardless of their trade, alarms, electrics, plumbing etc) are saying to me that something is knackered then I'll take their advice. In this case, you should take their advice because the charging circuit on that panel sounds f%$ked and you have no hope in hell of repairing it other than getting a new panel.