Okay Big Problem

My old Macbook Pro 2008 Silver Beelze has totally just blanked out. Model number is A1226 and so I bought a new Macbook Pro 13 inch 2009 Model Number A1278

So the question and problem that I'm having is this.
I have a a HD packed with Info on the old one I believe the HD is a 500 Gig 5400 RPM
I was wondering if anyone knows if I can just exchange the Hard Drives and it would just WORK like the old one used to. I'm not sure with mother board and all that other stuff and I surely don't want to replace the Hard Drives and having something occur like it just failing on me. This is a big problem if anyone on this forum can help me it would make me feel so relieved. Thank you so much,
Kyle Carlin.

You can't just swap hard drives because of the difference in hardware. However, if you have a Time Machine backup of your old drive, you can migrate the data to the newer MBP by using the Migration Assistant.

So what do I do about the broken screen? I didn't backup the files, should I use a HDMI Cable because if I'm not mistaken you have to go through system prefrences. :/

No, in that case you would want to use a Firewire to Firewire connection. Target disk mode works best for that. See the following Apple KB article: LINK

Thank you so much.

One last thing, will this be able to give my new computer my old software and make it just like the old computer was?

That does depend on your software and operating systems. For example PowerPC application will not run on OS X.7 or X.8 as Rosetta is no longer part of the operating system≥ Snow Leopard OS X.6 does support PowerPC software. For what it is worth get an external hard drive and use it for backups, either Time Machine or cloning,