MacBook Pro doesn't boot but passed hardware test

I have a 13" MacBook Pro, OSX 10.6 (Bought in UK in Dec 2009). It had been running slowly, I think because the hard drive was nearly full, but seemed much better after I deleted some files. Yesterday I was uploading some files to Dropbox, which were loading very slowly and crashed chrome - I think I remember it saying shockwave wasn't working. I tried uploading the files again, but the whole screen froze and I had to force shut down.

Since then it won't boot at all - just the grey screen, apple logo and spinning gear. I can hear the startup sound. I've tried the following:

Start in Safe Mode (Power+shift)

Progress bar stops at 1/4 and disappears, leaving apple logo and spinning gear

Startup Manager (Power+Option)

Shows Macintosh HD, and then Mac OSX Install DVD

If I select mac HD it returns to the grey apple logo and spinning gear

Reinstall OSX from disk (Power+C)

The same grey apple screen and spinning gear then slowly the disk loads. Have run disk utility, shows hard drive as as verified and when repair is run it says appears ok

I've run both the short and long apple hardware tests (Power+D) but they both report no faults found.

So, I'm stuck at what to do next. I don't have any files backed up (yes, lesson learnt) and my priority is to retrieve photos etc. I needed a new hardrive anyway, so fine to buy a new one. What should I do next?

Some options are:

Is there anything else I can do from the Mac OSX Installer? I don't want to delete my files! Can I check them from here?

Buy a FireWire cable and connect to another MacBook - should I be able to access my files doing this?

Buy a new hardrive and hardrive case. Remove the old drive and put in the casing. Install the new drive. Does it sound like my MacBook will work again with a new hardrive? Once removed what are the best ways to check and recover files from my old drive?

Any other ideas?! Really appreciate any advice!

Thanks.