Here is a link to the service manual for your recorder. This will help to disassemble the recorder to gain access to the switch to ascertain the problem.
If it is the switch itself that is the problem then here is the part number for the record button (I think,1-572-922-11, found on p.51 of the manual).
Here is a link to just one supplier of the part. It is not a recommendation to use them merely to give an idea of the price. There are others online just search using the part number only to get results. Scroll down about halfway to find the part.
58728 SON CC REC/PB SW 1-572-922-11 ANDREWS ELECTRONICS -1505 $4.50
Hopefully this is of some help.