The converter is essentially an AC to DC power supply with an intrinsic battery charger function. It supplies power to the 12V circuits in your rig - in conjunction with your batteries.
If your problem were 12v circuits, then the converter could be the culprit. However since your issue is with your 120V circuits, then the converter is not the problem.
But whenever you smell "that smell" it's never good, and something might be fried. Sometimes the damage is delayed... whatever was burning up might still work for a few weeks or months, but then when you need it most, it quits. Electrical problems such as this (as well as lightning, power surges, etc) can be finicky to troubleshoot.
Since you have lost 120V, the first thing I would ask is have you checked your breakers on the power panel? Have any of them tripped? If you are extremely lucky, this may be the only problem.
It goes without saying that while will not help you in your instance, this is a good reason why we should all have a good surge guard on board. The best of them will prevent the connection of the rig due to overvoltage conditions.
Best of luck in finding out your issue.