Corrupt project file, we feel your pain. Try these measures:
1. Transfer the project to a new disk.
2. Try to import the copied project instead of opening it.
3. Press CapsLock before you import the project (so AE doesn't try to preview the open comps), and then try to determine which comps are corrupt. I think you can hold down Shift (or was it Ctrl/Cmd) when you import the project to force AE to close all open comp viewers.
To avoid this in the future, do two things:
1. Enable "Auto-save" in the preferences.
2. As soon as you want to save, hit Ctrl-Alt-Shift-S / Cmd-Opt-Shift-S instead, and AE will "increment and Save" creating a new project file with a number at the end. This way, you can go back to earlier versions if you've hit a dead-end. I wouldn't work any other way...
- Jonas Hummelstrand