It sounds less like erection problems than desire problems, right? All sorts of things can affect desire. Conflicted emotions or deep-seated issues. Hormone levels. Men often have that low-desire problem when their testosterone is too low. Might be worth going to the doctor about. Or to a therapist, too, to talk about the issues causing his disinterest.

Lack of desire in men is a fairly common problem and not one to be embarrassed about. Or at least only if it's not something he'll seek help for, which is just silly when there might be help available. If he doesn't get help, as you don't believe in divorce, you're truly not going to be able to stay with him.

Cheating on him just disrespects him and your marriage, and if you consider the sad situation you're cheating on, I'd hope you'd feel awful about that. If you really have to have sex with someone else, get outta that marriage first. Otherwise, take care of your own needs playing solo for a while and strongly encourage him to get some help, explaining that you can't continue like this. Do the honorable thing and address it directly without cheating.