Connecting Hard Drives

Hello, I have a question about connecting 2 laptop hard-drives to a single laptop.

 

The problem:

 

My Dell Inspiron 7000 (circa. 1998) died.  I honestly don't think it's a hard-drive problem, but it's not just a battery problem ('cause we've tried replacing batteries and such and nothing worked).

 

I was hoping that I could take the hard-drive out of my Inspiron 7000 and connect it to my new Inspiron 600m (circa. 2005), so I could transfer all my old information to the new hard-drive.

 

There's quite a bit of information on my old hard-drive and I'm very nervous about loosing it.

 

If there is a way to accomplish what I want, would you advise me to do it myself or take it somewhere?

Thanks so much!!

~Luke