First, the notes would have to specifically state why the procedure(s) was/were not fully completed; that's kind of what drives the whole thing. Another thing to consider is the location the procedure was at (hospital, ASC, etc). Those things combined are what would send you in the right direction.
If this was in an ASC or outpatient, then you have to add the appropriate modifier depending on whether the procedure was canceled before (73) or after anesthesia (74), but there has to be a specifically documented reason for the extenuating circumstances that caused the procedure to be canceled AND the procedure would have planned anesthesia.
In order to qualify for a 52, the physician would have to discontinue the procedure by choice (not due to a medical cause, which would be mod 53), AND the procedure itself would not have planned for anesthesia. Anesthesia includes moderate sedation, by the way.
You should try to look for a better CPT code that more accurately describes the procedure that was done. Without better documentation, you're kind of backed into a corner.
On a side note, 93653 and 93656 cannot be billed together.