Well... lets just assume that you are buying a cheap POS 400W PSU and you are only running the LEDs on the 12V rail. Newegg's cheapest 400W PSU has a 20A 12V rail which is about 240W. An LED will typically use about 20-30mA and amber ones generally operate at about 2.1V.
So doing some simple math...
240W / 2.1V = ~114A / 30mA = ~3809 LEDs
(I may not have done this right, but I'm pretty sure I did)
Now this assumes near ideal conditions and that you know what you are doing. In other words, you should be able to get a lot of LEDs as long as you have some clue what you are doing.
May I ask why?