MOVs, like AVIs, are file packages. The videos inside these packages can be made up of any of hundreds of possible codecs, not all of which are editable in Premiere Elements.
MOVs from cameras, camcorders and phones should be editable. But many MOVs may use noneditable codecs.
Download the free program Media Info and not the resolution, frame rate, audio and video codec and video writer the program lists when you open one of your MOVs in it.
BTW, I'm assuming you've got Quicktime installed on your computer, which is a system requirement for the program.