The removal of the BSB dish and wiring I expect to not have any impact on what you have experienced, it sounds like coincidently something else has gone wrong, UNLESS there was an already loose mains cable somewhere which pulling out the old Sat cables made worse.
From what you are saying is it the main breaker in the main distribution that has tripped or just the RCD/MCB feeding the garage? Later post indicates it is the feed to the garage, not the main supply?
(I'm assuming there is a secondary distribution board in the garage)
Step 1: Garage isolated (all breakers off in garage), Main distribution board breaker for garage OFF, does the main breaker remains ON ? (if yes, then it is something on the garage circuit, if no, then it is something in the house)
Step 2: If Yes, then Garage isolated (all breakers off in garage), Main distribution board breaker for garage ON, does the main breaker remains ON ? (if NO, then it is something on the garage circuit from dis board to Garage dis board, if Yes, then it is something in the Garage itself)
Step 3: if Yes, progress through Step 2 but switching on separate circuits in the Garage distribution board to identify circuit at fault.
Cables do fail overtime, type of cable, its installation and water ingress etc Also breakers and switches can fail as well...
It's a bit hard to diagnose over the internet and if you are struggling to identify components in a distribution board then I would respectfully and strongly recommend seeking out someone competent who can help you in person. We can probably help with some rudimentary fault finding and sorry if I've jumped to an incorrect conclusion based on posts so far but last thing anyone wants is you getting hurt