I need a little help. I've put this off for far too long and I want to get some of my old Blender files and see if I can work on them once again. Problem is, the laptop they were on crashed some time ago. I don't honestly know whether the laptop can be saved, but in case it can't, I was wondering what the chances of my save the files on the hard drive might be, and also a ball park figure from anyone who knows how much this might cost would be greatly appreciated.

If they can be saved depends on what’s wrong with the computer and what kind of drive it is. If the drive is ok you might be able to take it out and put it in your new computer. 

I was thinking more along the lines of transferring the files from the old drive, if that was even possible, to a thumbdrive.

It does depend what kind of harddrive is in your lap top if it is SSD pulling the drive and connecting it to a PC or other laptop might be possible there are numerous types of hubs or cables you can use that you can connect up that drive using USB cables if it is M2.NV drive you might need to buy and enclosure that will treat that drive like it was a flash drive. Really need to know what type of drive is in the laptop. Another issue depending if the drive is corrupt you might need to invest in recovery software to try and recover those files off the drive and that will be hit or miss. But first and foremost need to know what kind of drive your dealing with to determine the easiest and cost effective route you want to take to recover the old files. 

I'm not qualified to try and start the laptop, so I'm taking it to a shop.

Sorry wish could have helped more good luck