I've collected years of data using a defective piece of equipment. How to salvage my thesis and graduate?
I'm afraid there's no magic bullet here; all you can do is proceed as transparently and reasonably as possible.
First, present clearly the proof that the machine was broken. After years of debate about whether the machine was broken, your committee has probably stopped following the interminable discussion. So, you should explain very clearly and unambiguously that the debate is over and the machine really was broken.
After establishing that, I think the main question you should be prepared to address is: why did it take you years to notice that the equipment was broken? Naively, it seems like you should have done calibration runs in the first few days and identified/fixed the problem right at the beginning. Clearly that didn't happen here, so you should proactively and clearly explain why not. Hopefully there is a good technical reason (e.g., there is no way to calibrate this equipment) rather than just a mistake on your part.
Third, consider whether there is scientific value in the procedure you eventually followed to diagnose the faulty equipment. If identifying the problem was not trivial, it follows logically that your successful diagnosis is a significant step. You want to find the right balance: don't inflate your achievement or gloss over any mistakes, but at the same time, don't sell yourself short.
Finally, you should definitely discuss this with your committee in advance. If your professor wants you to graduate, you will probably pass your defense. Still, your defense is not good to surprise anyone. Since you have firm time/budget constraints, any potential issues or objections should be identified as early as possible.