Chosen Solution

Vostro laptop runs noisily and overheats quickly and shuts down.

Noise - because your fan is working overtime trying to cool the cpu Shutdown - the cpu got too hot, so the computer turned off, hopefully to avoid any serious damage It’s overheating MOST LIKELY due to excess dust build up around the fan / heat sink radiator area. This is preventing the fan from dissipating the heat from the heatsink