Ok thanks for the info. I just took out the battery, held the power button down, took out and reinstalled both memory sticks, and then hooked up power to it. Unfortunately nothing happened still. When I plug the adapter into the laptop, I see the white light next to the plug come on. That bit of information probably won't help though. How much do motherboards typically cost for these things? And also, can I just install this HD into another laptop to get access to any files?

The hard drive does not need power from the battery to retain data.

Bad Battery is not going to crash a hard drive.

Replacing Battery or not has nothing to do with retaining data on a hard drive.

The machine should run without any battery installed.

If it does not then there are motherboard or other component issues.

Dell™ Studio 1735/1737 Service Manual

Its a LAPTOP Sata Drive.   You can use an Apricorn Satawire to access the data as though it were a Gigantic USB flash drive IF the drive is ok.

Manufacturer Part# : ASW-USB3-25
Dell Part# : A5274985

http://accessories.us.dell.com/sna/productdetail.aspx?c=us&l=en&s=soho&cs=ussoho1&sku=A5274985

Removing the Base Cover

1. Ensure that the computer is turned off.
   
   
2. Remove the battery (see Before Working Inside Your Computer). 

   <ADMIN NOTE: Broken link has been removed from this post by Dell>

   
   
   
3. Loosen the eight captive screws on the base cover and lift the cover off the computer at an angle as shown in the figure.
   
   

CAUTION: Do not touch the processor heat sink. Processor components should be removed only by trained support personnel.

Removing the Hard Drive

1. Follow the procedures in Before You Begin.
   
   
2. Turn the computer over and remove the base cover (see Removing the Base Cover).
   
   
3. Detach the hard drive from the system board connector.
   
   
   • For Hard Drive 1:
     
     
   • Remove the four screws securing the hard drive assembly to the computer base.
     
     
   • Pull the blue pull-tab on the cable attached to the system board to disconnect the cable.
     
     
   • Pull the black pull-tab to lift the hard drive assembly out of the computer.
     
     

Pull the interposer to disconnect it from the hard drive.

Will this method wipe out the contents on the hard drive?

Remove the battery, unplug the system and hold the power button for 30 sec.  Remove and reinstall both memory modules.

Verify that the LED on the power adapter is ON before you plug in the notebook end.  If it's not, replace the adapter.

Try powering up.  If it will without but not with the battery, the battery is faulty.  

If it won't power up after the above reset, replace the mainboard.

Red/White Flash = Battery is DEAD forever no charge FOREVER.

Motherboard Depends on which EXACT Model we are talking about.

Dell Studio 17 1737 MB Motherboard M826G F238N - 0M826G 0F238N - ATI VIDEO

http://www.parts-people.com/index.php?action=item&id=6767

Dell (F238N) Motherboard In Stock for $299.95

I'll have to see if I can stop by and pick one of these up. Thanks.

*One quick question. This isn't my laptop so I'm not 100% sure what this means. When I plug the adapter in, I notice that the little indicator on top of where the adapter plugs in comes on. Sometimes it comes on for a second and then stays off. Sometimes it flashes between red and white. What does that mean?

Ok here is an update. I had some time to take a look at it again. It now seems there IS a noise that was not previously there. When I push the power button, it almost sounds like the cd drive tries to operate and then it goes away. No lights come on and no display still. Does this change anything?

Before I decide what I want to do with this laptop, is there anyone who can answer my last question? Thanks

It really doesn't change anything - the system board is bad and needs to be replaced.