Based on what you have described so far (including the confirmation of bad capacitors as the source of the problem and that now it works for you):
- I don't know, but a 24-pin connector is really a 20-pin one with the CPU 4-pin connector appended to it. Some manufacturers (e.g. Antec) actually ship their PSU with a 24-pin connector that can be converted to a 20+4 set by sliding one of each other (pretty clever if you ask me).
- Because you happened to stumble on a standard DELL PSU connector?
- Yes, bad capacitors. It's very common in those types of PSUs.