I gather you've already bought the thing. So, part of the decision is already done.
Sure, see if you can get the old control to fire up at all, you should be able to tell from lights on the control panel, etc. Maybe scope some of the EGA signals to determine if H and V sync is coming out of the 9-pin plug. If so, go ahead and get the EGA-VGA converter and see what the control can do, whether it suits your one-off machining needs. I don't know the TNC-151 control, it apparently came in two flavors, one with G-code and not much else, and one with Heidenhain's proprietary language and their conversational machining package. The conversational thing may be what you would find useful. Practically no need for CAD/CAM in that case.
If the control doesn't fire up after the move, then you have to see how much time you want to put into finding out what is wrong. It could be a board wiggled loose during the move, or much more serious. Connectors and tantalum capacitors are the two big problem areas in these older systems.
Jon