I have 2 compaque presario cq61 laptops. One has a dodgy screen the other a dodgy hard drive. Can I just pop the good hard drive from the dodgy screen one into the other?

If same models as you state, should not be an issue

Go to the Compaq site and run your P/N on each. The biggest problem you can run into doing something like that is chipsets or architectures. Some companies have several hardware options for a single model number... the hardware needs to be exact, or pretty close to it.