My grandmothers White Super Lock 534 and it will not sew what do I do?

First thing to do is get a manual. One can be had here:

(I don't know, if you don't have a manual, how you can be sure it is threaded correctly. Serger threading is complicated. How long since your grandmother used it and/or had it serviced?)

Next, follow instructions in the manual for a thorough cleaning and lubricating. If that does not unbind it, take it to a reputable repair person. Depending on where in the world you are, I recommend Ron:

Ron Anderson A1 Sewing Machine

18 Dingman Rd Sand Lake, NY 12153

NAYY, HTH

Sounds like it needs a quick trip to the serger mechanic. It's probably "sat" in one position long enough that there may be problems with the internal lubrication. You may also have a looper timing problem.

is the manual for the machine (Singer has White manuals on their website). Maybe Ron or someone who has had one will pop in to tell us if it's worth the bench fees to get it serviced. Some older sergers definitely are, some may not be.

Kay