I'm not just 100% sure what is going on here, but here's my best guess.
Generally, when you download a file, you first get the option to "save" or "run". If your operating system (vista) is not giving you this option, but instead is going immediately to the save option and then asking you where you want to save it, then it is probably the case that whatever you are trying to download is some file that the computer doesn't know how to open.
Because of your use of the word "play", I'm imagining that you are trying to dowload some kind of .mp3 file, or .wav, etc -- something that is to be played with Microsoft Windows Media Player, or quicktime, etc., and vista seems to have forgotten that it is supposed to open the "whatever-type-of-file-it-is" with media player, or quicktime, or whatever.
If this is the case, the fix for this is in the control panel -- Go to the Start menu, then the Control Panel, (Click on classic view if you're not already in it), then go to Default Programs (may have to scroll down to find this), then choose the option to "Associate a file type or protocol with a program."
If it's an .mp3 file (or any other file for that matter) that you're trying to dowload (and play rather than save), scroll down the list until you find ".mp3", and make sure that it is set to open with whatever program you want it to open with. If it says that it opens with an "unkown program", or some other program that you don't want it to open with, then choose the "change program" button at the top of the menu, and then hunt down the location of whatever program you want to open .mp3 files.
Even if your computer was previously successful in opening whatever file you're trying to open (rather than save), sometimes these settings can get mixed up. Also, sometimes the program that was previously used to open a particular file type gets deleted, or whatever.
At any rate, let me know if this doesn't fix the problem.