Repair or replace Toshiba laptop?

OK drivers are software, a program that controls a device, so I am really confused as to what he is telling you. Sounds a tad fishy to me. Drivers don't cost that kind of money. Usually they don't cost anything. Very Odd.

Now if a part needs replacing (hardware) that is a different story.

If you want to keep this laptop, and if it is repairable, then you need to replace the fan first, otherwise you will fry the machine. Next, you need to see if it will start up in "Safe Mode". If it will, then you should update the drivers. If it won't, you may well have fried the graphics card and need to replace it.

How to enter "Safe Mode" when booting the computer.

In Windows 8 and 10 ...

As your computer restarts, press F8 (possibly a few times) to enter "Safe Mode"

a. Press the "F4" key to Enable "Safe Mode".
(The computer will then start in "Safe Mode" with a minimal set of drivers and services.)

b. Press the "F5" key to Enable "Safe Mode" with Networking.
( Once "Safe Mode" with Networking starts, Windows is in Safe Mode, with additional network and services for accessing the Internet and other computers on your network.)

c. Press the "F6" key to Enable "Safe Mode" with Command Prompt.
(In "Safe Mode" with "Command Prompt" starts Windows in Safe Mode, with a Command Prompt window instead of the Windows interface. This option is mostly only used by IT professionals.)

Now sign in to the computer with your account name and password. (If you have one set.) When you are finished troubleshooting, you can exit "Safe Mode" restarting your computer.

If, the parts needing replacement, and the labor to do the repair, come to more than say 1/2 the cost of a new machine, I would consider a new laptop.

Oh, and if you want to go to a tech/or repair shop, I really would try someone other than the one you went to before.