The Bose system does seem to suffer over time. The amp for the cabin speakers can suffer from dry joints, providing distortion or no sound, usually worse when the amp is cold. The speakers themselves often just give up. The sub has it's own separate amp inside the sub enclosure. This can also be unreliable.
firstly I would check the sub is actually connected. A lot of the subs in 8L's would have been messed around with, unplugged in leiu of an aftermarket install and may not have been plugged back in when the original system was put back in.
If the connection seems OK, check that the connector is receiving 12v perm live and 12v switched live when the HU is on:
If the lives are OK then chances are the amp or the speakers are at fault. Remove the front of the sub and check the impedance of the speakers, should be 1.5-2ohms. Also push the speaker cone inwards and check it is a smooth movement, not crunchy. If the speakers are OK then it must be the amp.
You can buy a replacement Bose sub and amp on ebay for around £80.
You can then use the speakers in the faulty sub to swap for the dodgy ones in the front door cards as they are the same unit.
The cabin amp can be repaired by reflowing the main solder joints, or a replacement found on ebay for around £40.