Video from still cameras often employee codecs that are designed for compact storage and this video is not made to be edited.
Your camera records in H.264 MOV, a very challenging format for Premiere Elements to work with. Quicktime Pro, as you've seen, can handle these files easily, however, because this codec is part of Apple's codec library.
To convert the file to video which can be edited in Premiere Elements, save the files as DV-AVIs. DV-AVIs are the ideal format for use in Premiere Elements using the standard DV project preset.
Thank you for the response, in saving to another format will I retain the same quality and clarity as my original, or have I been spoiled with out hope?
Using Quicktime Pro for the conversion and using DV-AVIs in Premiere Elements, you should get excellent results!
(Note that this will convert your video from hi-definition to standard definition video -- although, unless your output is to a BluRay disc, you'll find that standard DV gives you the most efficient workflow with the cleanest results.)