HP laptop failed HDD - use desktop to recover files?

I have a HP Pavilion g6. I am not knowledgeable when it comes to hardware. Not even a little bit. But from what I've been reading on here, I'm pretty sure I need to replace my hard drive. I have a few questions, and really appreciate anyone who can help me! Please understand I'll need really specific and basic words, as I'm uneducated in this area.

1) Is it possible to recover files & photos on my laptop by using my desktop? The laptop runs Windows 7, the desktop runs Windows XP.
2) If I can't recover my laptop files with my desktop, how do I recover them?
2) Does it make sense to replace the hard drive or should I just buy a new laptop? I'd rather do the least expensive thing, naturally, but if replacing the hard drive will only buy me a short period of life on the old? (2.5 years) laptop, then I'd rather replace it. I'm not sure of the average lifespan of a laptop.

Result of the HP Advanced System Diagnostics test:
Hard Disk Test
Testing Drive: 1
SMART Check: FAILED
Hard Disk 1 Hard Disk Test: FAILED

System Information:
Model HP Pavilion g6 Notebook PC
System ID 1693
Product ID LV860UA#ABA
Warranty Start Date 04/15/2011
Processor Type Intel® Core™ i3 CPU M 380 @2.53 GHz
Processor Speed 2529 MHz
Memory Size 4096 MB RAM
BIOS Date 01/16/2013
BIOS Revision F.37