The invertors can be fussy about bad tubes and they usually stop oscillating until the problem is fixed. I'd suggest checking for anything obvious like blown SMD fuses on the invertor PCB, see if you can get a shock from the FL connector etc.

If the FL(s) appear darkened then that can be a sign they're bad but it's not conclusive. Might be worth taking a look at them just in case they're physically broken. Here's somebody on eBay selling FL tubes