Problem With An Auto Repairer

[XCGS351]

I had a problem with my car that it only starts intermittently. So I took my car to an auto repair shop to have it fixed which is owned by a well known insurance company.
They replaced the starter motor because that's what they reckon was the problem, but when I went to picked the car up, paid their fee, went to my car and what happens, it won't start.
Went back to the office I told the guy at the counter what happened, he sent the mechanic to have a look and sure enough when he tried it, it wouldn't start.
So my car was left with them for another two days to sort it out.
In the end they couldn't find the problem, reckon it started all the time in the two days they had it.

What I would like to know is that should they refund the money I paid them for something that wasn't the problem in the first place. They know they misdiagnosed the fault they know the car didn't start even after they replaced the starter motor yet they say it to my face that the starter motor was the problem (this after I told them what are they going to do about the repair I paid that didn't need to be done).

They done wrong but wont refund the money, does anyone thinks that's fair?