According to your other thread Issues with packard bell all in one l5351 ,it looks like it might not be your CPU cooler is the culprit.
<< My packard bell all in one l5351 was making a hell lot of noise >> What sort of noise is it? Have you checked the condition of the HDD?
<< CPU #0 93°C. Its just shut itself down again >> It doesn't look good ,the CPU is overheating & might be on the way out.
<< I have a feeling that the metal cover is putting pressure on the fan, because when I first opened it, they was a big black circle on the metal which indicate that it was directly on top of this fan >> The big black circle on the metal is just a heat ring mark from the heat dissipated from the CPU, the metal cover isn't putting pressure on the fan.
<< I was wondering if the heat size I found on amazon will fix? >> No,it won't fit. You'll need an AM3 cooling fan.
If you can still get it up & running ,can you go into Bios and tell forum members more PC hardware details by expanding the Product Informations such as which model of CPU being used?