First, welcome aboard. It's good to see you here.
It's been maybe 20 years since I had a TH350 open.. but, there's at least 2 manual that can provide you with the test procedures to help you diagnose your problem.

And of course there's always youtube, I haven't done any searches there but I'd bet dollars to donuts you'll find something there.

I can't say I've ever seen or heard of that cover "popping" off. Which kit did you install? Changing shift points only or shift points and pressures? B&M kits are very reliable, usually they install with no issues..

Hope it helps and let us know what you figure out.