Where can you cheap make a laptop error analysis?

My laptop I bought at MediaMarkt does not work anymore.
After plugging in an HDMI cable, it will not turn on. Does not make any noise and otherwise the screen stays black. Only the battery light is on.

Not the first time that he gives up the ghost, but I have no guarantee now.

But I definitely need the laptop for my work. Since I'm financially short of cash I'm now looking for a workshop that can tell me what is wrong with my laptop. However, this should not be too expensive.

(It's only about the error analysis is not about the repair)

If it is important I live in Halle, near Leipzig.

Freital Poisentalstraße.