I was planning in removing the psu of the dell dimension and putting it in my hp pavilion a350e. You guys think this might damage something or it won't work ^^?
It's good for you that you asked!!! NEVER, never, never, never mix Dell power supplies and (any) other maker's motherboards!!! Or the other way around - NEVER mix Dell motherboards with ordinary, standard power supplies. In either of these scenarios you will destroy the hardware and the power supply.
Dell deliberately wire up their PSUs and motherboards differently from everyone else, but they use standard power connectors, and they don't warn you. The first you'll know is when you press the power button and nothing happens except a burning smell.