If the MCP5000 and Terminal 5000 work fine from your link room, the problem sounds like it is definitely the IR receive circuit of the BM5000 itself. Since the BM5000 was very popular, you may want to find a replacement on eBay. Just an option if repair is too difficult or costly.
BeoSystem 5000 (BM 5000, BG 5005, BC 5000, CD50), BeoCenter 3500, BeoCenter 2500, BeoLab 2500, BeoVox S-45, S-45.2, RL-140, CX-100, CX-50, C-75, 3 MCL82 link rooms, A8, 4001 relay and ambio