The transformer is probably okay. There should not be any continuity between the primary and the secondary on a normal transformer. Raw resistance only gives a rough idea of the viability of a transformer...the real measure is inductance, but that takes other tools to measure. I think you need to look for something else to figure out what's going on. Even if you input the 120vac, the output would unlikely be the 11.5 unless it was under load - it would likely be somewhere near 15-18vac with no load, but that's dependent on the core design. Transformers are often used as inputs to a power supply. Without a schematic, it's hard to know what's going on.
Important note - I'm not a pro
Retired Defense Industry Engineer; Schluter 2.5-day Workshop Completed 2013
What I would typically do if something is not working is measure the voltage at the primary for 120 VAC with a multimeter.
Then measure the voltage at the secondary.
Then go from there.
Very rarely have I ever needed to replace a transformer for a non-working electronic power supply. Usually no main power, fuse blown on the electronic circuit board, capacitor, or voltage regulation components (main power regulating transistor).
What is the problem you are having?