When I turn on My laptop the laptop’s fan speeds up to max speed it can go at and the caps lock light is blinking and the screen doesn’t turn on

If it is a HP laptop (or any other), it normally means a Power issue.
Visit to a service centre may be a must.
 
The processor generally uses a heat sensor to determine the speed of the fan. The hotter the CPU gets by whatever load you put on it, the faster the fan runs, like a thermostat keeps a house cool. If your fan is running at full speed and you aren't using many applications you might have the fan clogged with dust or a hardware failure. Check your laptop manufacturer's documentation and see if the blinking caps lock light is an indication of a hardware failure like a beep code is for some memory issues on some pcs. Also, there would be a diagnostics program you could run on bootup depending on the manufacturer. Maybe just a clogged fan best case scenario, worst case scenario hardware failure. If you do run a hardware diagnostics program don't forget the lcd issue too.
 
The processor generally uses a heat sensor to determine the speed of the fan. The hotter the CPU gets by whatever load you put on it, the faster the fan runs, like a thermostat keeps a house cool. If your fan is running at full speed and you aren't using many applications you might have the fan clogged with dust or a hardware failure. Check your laptop manufacturer's documentation and see if the blinking caps lock light is an indication of a hardware failure like a beep code is for some memory issues on some pcs. Also, there would be a diagnostics program you could run on bootup depending on the manufacturer. Maybe just a clogged fan best case scenario, worst case scenario hardware failure. If you do run a hardware diagnostics program don't forget the lcd issue too.
Seems that the computer has not yet come on. It is not likely to be a hot CPU.
 
The fan spins and lights blink which indicate that power is being supplied to the pc, granted the cpu might not be involved, especially with a blank lcd.
On a normal startup, the Caps lock will NOT flash continuously. The keyboard lights will flash once.
A flashing Caps Lock is a sign of power issue.
 
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