frigasaca, I think that is totally up to you. But, it will not be cheap. The advantage is he can see and hear what is happening and he will have extra power supplies, graphics cards, ram and all that stuff to replace one at a time until he finds the problem. But, you will pay a lot for that, and you have those things or friends who do that could help you do the same thing. We cant see it or see what it is doing so have to depend on you to be our eyes and ears, but we can do the same thing for free, if you have friends that will help you.
One of the first things a shop will tell you is something you already know. Your computer is getting to the age where components wear out and needs to be updated to newer components. But, you really don't need to pay someone to tell you that, nor do you need me to tell you that. If we can find the component or components that need to be replaced, you can fix it yourself, and we don't charge anything. This site has some of the best hardware experts there are. Britton30 and I have probably built more computers, taken more apart and fixed them than most shops have, and there are many others here who have done the same or more. In fact, I finished building one yesterday and Britton30 is building one right now. We do no only not get paid anything for what we do, we wouldn't accept any money if you offered it. You are on the best tech support site on the INTERNET and it's free. But, the downside is you have to do the work and put the time in to do the tests, which can be considerable. So, you have to make the decision. The real problem is not fixing the computer. The real problem is finding which component needs fixing. That often requires a lot of lengthy tests and some experimentation. It is also going to require you to realize your computer is older and built for software that was made 10 years ago. The newer software is much more demanding than what your computer was built for.
At this point, it seems as though your problem is Graphics related. That could be drivers, the power supply not putting out enough power to the card when under stress or the card itself. Part of that can be easily determined. If you have another card, preferably one with the same or similar power requirements as what you have, or have a friend who has one that will loan you their's or swap cards with you, you will know very quickly if the card is the problem. The same with the PSU, or you could pay someone a lot of money to do that for you. The choice is yours.