So, I have looked a little deeper into the BT Cheetah, from what I can see it is almost a perfect copy of the LO3000 - pictures to follow.
I have cleaned a lot of the dust and dirt from the PCBs inside the machine, and have repaired a problem with the X2 capacitor fitted inside the power supply.
This far, the power supply is giving all the correct supply rails to the motherboard (tested by removing the line interface card to get to the test points on the motherboard).
I have substituted the battery supply from the battery back up with my bench PSU just to make sure that everything is getting power where it should.
However, this is a poorly machine

I think there might be a problem with the CPU at the moment - either the eprom containing the data for the TP is dead, or the processor has a problem.
Does anyone with experience of the LO3000 have any ideas where to turn?
Thanks
Sean