You have a 2000G control, not B. I have a lathe just like this. Although not as easy or user friendly to setup and operate as something newer, it is very accurate and has been very reliable.
Unfortunately the DB25 connector inside the tape reader box is for a tape puncher. It is not an RS-232 port. These machines did not come with RS-232 capability built into the control. I believe the later model 2000GII did but that control also had a CRT, pretty much a different beast.
I think the computer you speak of being hooked to the lathe may have been a system like this one,
RYM - PC-DNC Editor MPE - BTR solution for older Fanuc and Yasnac CNCs
It connects a PC to the machine control via parrallel printer port (the tape reader is a parrallel system). I don't use this style on my machine so I can't help anymore here. I prefer the ones made by Advanced Digital Research, Inc. M2M & DNC Products. Although expensive, they work very well and can be configured for just about any machine out there.
Hope this helps. I would try contacting someone at ww.rym.com. They can probably provide much more insight on this.