Some ideas for debugging things:
- did it used to work? then look at the deltas; what changed from working to not working?
- use logic and deduction to narrow the problem down. break it down into a list of components or sections. it can be valuable to isolate or bisect your design until you've found the failed component or subsystem
- work backwards: measure the failure and assess what are the inputs. measure each input, repeating until you've worked your way all the to the failure
- top down: if you know what output is failed verify all the inputs are correct and work forward until you've found the failure
- scorched earth: verify everything, what's left is what's broken
Advice:
- find a way to reliably and quickly repro the problem
- involve the team and involve the vendor right away
- be organized, take notes