Let me be straight with you: a 2011 notebook is worth maybe 50-100 reais on a used site, so charging a thousand reais to try to fix it is absolutely ridiculous. The technician is offering you a service, not a guarantee of results. Legally he can charge for his work hours even if he can't solve it, but in the case of an authorized service center, they should be more transparent about this before touching the device.
What I'd do: first, ask for a detailed written quote before anything else. Ask exactly what he's going to do, how long it takes, and what the real chances are of it working. If he says he doesn't know without opening it, that's fine, but then he should only charge for the diagnosis, not the "attempt". If they insist on a thousand reais without giving you clarity, find another smaller repair shop - independent technicians tend to be cheaper and often solve the problem for way less.
Honestly, if the repair cost ends up close to the price of a decent used notebook, it's not worth it. But before you give up, take a photo of the exact model and check forums or YouTube videos to see if it's a common problem that's easy to fix. Sometimes it's just a dead battery, loose connector, or something like that.