Go to Adobe Reader site, and try to download any updates with it. Also their help section might be able to help. My husband tells me that some programs won't work with others, such as with Spybot Search and Destroy, and Ad Aware. When 2 programs don't work together one might keep the other one from opening. You might want to see if another program you have on your computer is keeping Adobe Reader from opening. You also want to check your program files to make sure when you uninstall Adobe that you get it completely off the computer before reinstalling it. One other thing I usually do before downloading a new program, or one that I am having trouble with is to run a virus scan, and a Spybot S&D scan before installing the new program, just to make sure that there are no viruses or such that are interferring with or corrupting the new download, once it is on my computer. I've had a file with a trojan virus mess up a couple programs on my computer. I had to ghost my whole computer, taking it back to a time when the computer was free of viruses, then reload all my programs once again.

It could be your properties, go to a file and right click go to properties and make sure that adobe is the program it is to open with, if it isn't click the change button and click on adobe to make it,
I have had this happen with different files the properties just decides to change itself. hope it helps

Maybe your harddrive needs a clean up.
I would try to uninstall the complete program (and other junk you maybe not even know about), clean up, then download the newest version or Adobe Reader and install again.
A free registry cleaner is available from Piriform.