I am on a windows 32 bit computer windows vista. I am required to submit a project and it HAS to be able to convert from windows to imac! Quicktime is preferable but anything that can convert would be wonderful. I need a reply by tomorrow. I do not own and am not willing to purchase any form of expensive software such as adobe to fix this problem unless it is an ABSOLUTE last resort. please help.

Given how little information you provided, I will make some assumptions...

You have an animation in Blender that you need to render in a format that can be played back as a movie on an iMac. Correct?

I believe that an iMac (using Quicktime as a player) should be able to handle a generic MPEG.
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Spacemice Wiki -- Input devices for a 3D world.
Spacemice / Blender Compatibility

Use ffmpeg. Or if you need a girly-man GUI, Handbrake.

For a player, VLC is a free download and can play just about any format worth playing. It's probably preferable to QuickTime.

For the encoding, have Blender render to individual frames in lossless PNG format at a minimum. Then you can use something like FFmpeg to encode it to your choice of delivery formats. Don't have Blender render direct to the delivery format, otherwise you'll have to redo the rendering as well as the encoding if you change your mind about the latter.