Computer cases, motherboards, and power supplies for the so-called "White Box" PC makers were standardized by the "ATX" patterns from about seven years ago or longer. It's the Small Form Factor, HTPC, and micro ATX systems that are less standard (and most of the brand name manufacturers make the choice to sell their own non-standard proprietary styles of parts).
You shouldn't have any problem with the power supply fitting in your 1999 box.
:beer: