Is it possible to retrieve my desktop files from my spoiled laptop?

Most likely yes, in my take, a computer has a built-in retrievable content where you can find it over it’s back-up drive. You can search your files over the computer’s back-up storage. So, most likely you’ll be able to find the file that is in the slow laptop. You can also install a file finder over download.com that enables users to track old files that are hidden over sluggish devices.

Oh yes because the laptop is working the same with or without a display, but you simply cannot see it. The easiest solution is to attach an external monitor, which should plug into a port on your laptop. Then you simply transfer the files onto a flash drive and move then to wherever you wish. If you do not have a monitor, simply take the laptop to a friend's house and borrow theirs.

It is still possible. The memory is stored in your hard disk. As long as it is in good condition, you'll be fine.but if you don't know what you are doing, better call a technician to solve your problems.