A device (or motor or machine) is broken, so we say to the person with the broken device:
- I'll get it working again. [because it is not working now]
OR
- I'll get it to work. [because it doesn't work now]
Dialogue:
John: My computer seems to be on the blink. Can you get it to work again?
Billy: Yes, I can get it working again quickly.
OR
John: My computer seems to be on the blink. Can you get it working again?
Billy: Yes, I can get it to work again for you.
So, either can be used. There is not any essential difference between those two dialogues.
For example:
I have a new dishwasher and I push the on button and it does not start running, and I say to the repair person: Can you get it to work? He answers: Sure thing, I'll get it working in no time.
If a new machine, device, motor etc. has not worked when you turn it on the first time, you cannot get it to work. Here, we wouldn't usually say: get it working in our description of the problem.
However, the second one has an additional meaning.
to get something to work is not just about devices, motors, etc.
A relationship can be said to not work. For example, you've been disagreeing with someone about your relationship for a while, so you might say:
- We should make an effort and get it [the relationship] to work again?
OR
- John doesn't think he can get his relationship with Ada to work again.