MOV is a wrapper... what is inside your wrapper?
Codec & Format information, read both links in reply #1 http://forums.adobe.com/thread/1270588
Report back with the codec details of your file, use the programs below... A screen shot works well to SHOW people what you are doing
http://forums.adobe.com/thread/592070?tstart=30 for screen shot instructions
Find file information for PC/Mac http://mediaarea.net/en/MediaInfo/Download
Do you have Premiere Elements 10 and 12 on the same computer?
It is important that you have QuickTime installed on the computer where Premiere Elements is installed. This point goes to Sandeep's question to you. If you have both versions on the same computer and QuickTime is installed on that computer, then that directs into other troubleshooting paths.
What are the properties of these .mov files and what is the brand/model/settings of the camera that recorded them. What have you set as the Premiere Elements 10 project preset. The project preset should match the properties of the source media. In Premiere Elements 10, you get to set the project preset in the new project dialog. In version 12, the program takes over that function, giving you a project preset based on the properties of the first video drag to the Timeline.
So, what are the properties of the source and what is your intended export for your Timeline content.
Answers to the above will help us to customize reply to your situation.
Please ask questions and ask for clarification for anything written if there is anything that you do not understand in the above.