Why won't my computer (Mac OS X 10.4.11) properly download or install programs?

I have tried downloading several programs on to my computer (google earth, audacity for mac), and the .dmg files do appear on my desktop. I can open the .dmg files and copy the actual program on to my hard drive, but when I click on the program it will not open. This happens no matter if I try to click on it in my hard drive or on my dock. When I click on it in my dock, the icon bounces once and then stops, as opposed to other programs which bounce a few times and then open. In the top left corner the word "Finder" stays there instead of changing to the program name like it should. If the information helps, several of the programs that used to work on my computer (photoshop, acrobat) have spontaneously stopped functioning. This happened at the same time that I was suddenly unable to download programs. Any suggestions would be much appreciated.