The computer made lots of noise before it died, actually shaking the desk in its death throes.
Sounds like a problem with a fan.
Could be a fan in the power supply.
Could be a fan on the video card.
Could be the fan on the processor.
Could be a case fan, though that's less likely to keep the computer from starting.
But it does sound fixable.
Computers can last far longer than seven years, though power supplies usually don't.
Whether you'd benefit from a new computer depends on the type of games you play.
Good luck.