Most of the 'DELL's of the world have custom sized PSUs which are designed to fit in the spaces that they fit in. As such - a standard PSU will likely not fit into that same space. That leaves you with two options. Find a replacement based on the current model number and size of your PSU or purchase a new case and PSU and move the guts over to the new box.
You should be able to get the model number off of your PSU and do a quick google search. From that - you will get the exact size and see if you can find what you are looking for. Based on this - you won't have many options for a quality manufacturer (as you would with a standard PSU) - but you may be able to find something that will work.
The second option is prefered - as you will be able to get the quality that you should have from manufacturers such as Seasonic, FSP, Zippy or Superflower. Additionally - since DELLs (and others) are so tightly packed, you will have better airflow and longer life of your existing components.
If the size of your current PSU is actually standard - then you simply need to purchase a quality PSU from the manufacturers above and re-wire your DELL.
Good luck.
UPDATE: Seems this thread shows that it can use a standard PSU:
http://www.tomshardware.com/forum/210472-28-replace-dell-optiplex-gx620-305w
Read this and find a PSU made by the manufacturers above:
http://www.tomshardware.com/reviews/power-supply-psu-brands,3762.html
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