Be aware that the firmware of many drives terminates spin-up if some serious fault is encountered (for example, if it is unable to move the head to track 0). If it doesn't pass the basic self-diagnostics, it figures that there is no point in spinning up all the way. Seagate drives seem to have particularly fussy power-on diagnostics, but other makes behave similarly.

If it is just a case of stiction, then you may wish to find the current-limit resistor Wally mentioned, and reduce it in value. This hack was useful in getting some old 40MB and 80MB Quantum drives to work much longer than they had a right to. I never did any detailed experiments, but cutting the resistor value in half (by paralleling it with another of the same value) seemed to work ok.