Dell inspiron N5010 display issue

Hello,

I have an inspiron N5010 laptop (out of warranty), which was working fine all these years.

Unfortunately, yesterday when I tried to turn it on, the system initiated normaly but the screen remained blank and then it started beeping 8 times every 3-5 seconds. According to what I found online, 8 beeps indicate an LCD failure. When I tried to connect it to a TV monitor via HDMI cable nothing came up, the monitor detected the connected device but it had no signal.
Since the screen is blank, I cannot run the diagnostics neither enter the BIOS setup. In case of an LCD failure I could replace it by myself, but I cannot be sure if that is the problem. Could you please tell me what can I do to distinguish if it is LCD or GPU failure?
I have to mention that the laptop was suffering from overheating, hence I used a cooler to reduce the temperature.

Thanks