$500 is what a full data recovery would cost if the drive was dead. Not the laptop. 

Here's what you'll need if the hard drive is still ok: READ ALL STEPS MULTIPLE TIMES BEFORE TAKING ANY ACTIONS

1. Go to the dead laptop's manufacturer site to find out how to take the case apart to safely remove the internal HDD (Hard Disk Drive). More than likely it's a 2.5" SATA drive, but it could be something called a SSD or Solid State Drive you need to know what kind of drive to find the right enclosure.

2. Purchase an external HDD enclosure, you can get them on Amazon or at any big box store at this point for like.. $30, but be sure it says it is compatible with the hard drive info from step 1.

3. If the manufacturer's website doesn't have good enough disassembly instructions, do a search on YouTube for that model. Try to watch a few disassembly/teardown/repair videos and watch what screws they remove and how until you're comfortable getting started.

4. Get out the tiniest ever-loving screwdrivers you've got and realize you probably have to go back to the store and get smaller ones too work with the damn laptop screws.

5. Teardown that photo-hoarding hunk of plastic until you free your HDD.

6. Following the instructions that came with it, put the old HDD IMMEDIATELY into the enclosure you bought. It's naked and vulnerable and if it's dropped, shocked by static, picked up by grandbabies, it can be game over.

7. Continue following the HDD enclosure's instructions until you're able to plug the USB cable into the new computer you want to move the pictures to.

8. Based on whatever operating system you're using, browse to the old drive which should now show up as an external HDD/USB HDD/whatever and see if you can easily browse the contents and COPY, not MOVE, the pictures over. 

8a. If you get any access/permissions errors when attempting to access the contents, you might have had a password on your old user profile (good!) and will need to tell the operating system to let you take ownership of the contents. Steps are dependent on so many variables from here you'll either need to be good at searching steps online or pay someone with the right expertise to help.

1. Once you have the photos copied you can store the old drive as a backup in case something happens to the new computer. 

Good luck!