HP India — Pavilion Laptop

I bought this laptop in March 2021. Since that day, I have been facing the issue of blue screen. All of a sudden, my screen hangs and it automatically restarts. Sometimes it shows a black screen and just stays still—no restart, no shut down.
My laptop was under warranty for 1 year. From March 2021 to March 2022, I called HP customer support at least thrice and explained my problem. Every time they ask me to have a data backup and install Windows again. Even if I explain to them that this has already been done, they will still say the same thing.
I thought if I would show it offline to the local HP customer support center, it might improve, but they performed the same window reinstalling function and gave me this laptop back.
The laptop works completely fine for 3–4 weeks after performing the function. Later, I ran into the same problem.When I lodged the complaint in March, I explicitly told the customer support team of HP that I had been facing this issue for a very long time. Now its warrantee is going to expire soon, I want a fix solution. They made me believe that now my laptop would work efficiently. After performing the window reinstalling again, it worked well for 6-7 weeks. I was relieved that it was finally working properly, so I informed the customer support team that I was satisfied and that they could close the case ID.One week after that day, the problem struck again. My guarantee had expired and I was left with nothing.
Now the HP customer support team is telling me to extend the guarantee and then they will see the problem with the laptop.
My question is
When it was in guarantee before, why didn't they provide me the solution? WHY SHOULD I TRUST THEM AGAIN? Is it some kind of strategy not to provide a solution in the guarantee period and later ask for an extension of the guarantee to ask for more money?

I have been facing the issue for more than a year. I am a student at IIM Nagpur. I have a lot of work to do, lots of quizzes and submissions, but the dysfunctionality of this laptop has hindered my learning and growth.
Moreover, the HP customer support email id that is shown on the internet doesn’t work. The email ID is [protected]@customerservice. Whenever I try to email HP officials, it does not work. I have wasted my time on calls explaining my problem to these people but never got a solution.
I need justice.