The previous owner did a bad job, painting the interior of the house. Paint has bubbled, peeled and flaked off, walls, door frames, etc., etc.. The thing is, half of it, is stuck fast and isn't going to come off. The other half has come off.

Clearly, they didn't use primer. What do I do? Do I remove the whole lot, either chemically, or with heat gun? Or can I just put primer on the bits where it has come off and then paint over the whole lot?

I am new at this (as you can tell).