cycling 4 LEDs at varrying speeds

do you have a link to millis()

Sure: millis() - Arduino Reference
(I'll bet you could have found that...)

and when I removed delay() the LEDs all lit up and stayed on.

Getting rid of delay() requires more than the delete key. Look at the blink without delay example. Slowly blinking LEDs with nary a delay() in sight.

That is what you need to rewrite your code to do.