It is a very easy fix, once you get the BM24 out, you will see torx bits holding on the casing. Basically, when the torx bits are out you can remove the casing and see the underside of the circuit board.
You will notice that there is a small circuit board (I have heard it referred to as a daughter board) attached vertically to the main circuit board and on the underside of the main board, you can see the solder where it is connected - There are 7 big blobs of solder in total in a horizontal line. They are grouped as follows: [single blob ------ 2 blobs together --------- 2 blobs together --------- 2 blobs together].
Here is a pic off the net showing exactly what I mean:
These blobs of solder will have become 'dry joints' meaning they will have cracked. You may or may not be able to see the cracks but its 99% certain that its happened and that is your problem.
I bought Argos' £3.99 soldering iron as it has a sharp fine tip, and then just some regular solder. All you need to do is heat the blobs until they become runny and then add in a touch of new solder to the joint once the existing solder is 'liquidey'. Do this on all 7 of the blobs (in fact where there are 2 together they are so close that they are almost like 1 big blob).
Once the solder is dry you will have better joints which shouldn't dry out again as the modern solder you have mixed in is more resistant to the lead free stuff they were using 10 years ago (i.e. when the BM24 was manufactured)
There are repair services on ebay that do this for £39.99 and even they admit that its cheap because its such an easy fix (not like the BM54).