When you open it on another computer, try saving it with a different file name and then opening that one on your machine.
Try opening it on your machine using CC 2014 and see if it behaves.
What plugins are you using?
Is everything in the project created in AE or are you using Illustrator files, Photoshop files, JPEGs, etc.?
Tried all of that, Sometimes works, sometimes doesn't.
I also tried removing all plugins (only used a crop from Creative Impatience) and fonts. Still no go.
I think my next issue is to uninstall CC then reinstall. It's just odd that it's only this individual file on this individual computer.
Reinstalling is one thing to try.
Do you have any scripts installed in your ScriptUI folder?
I removed the entire scripts folder, it opened. I made a change and saved, closed it. Reopened AE and it crashed again on opening the project.
What happens if you import that project into a brand new project (and save it under a different name)?