OK, got the model.
Have you actually tried booting from the SL 10.6.3 disc (insert disc, restart and hold down the C key no later than the chime). Keep C held until the Apple logo appears.
I ask this because I'm not entirely clear if your error is with the physical drive or the software application DVD Player. If the latter, it plays no part in booting from the DVD.
With a broken DVD drive I don't see how you're going to install on the external, either.
SL has never been available as a download. (not to be confused with the updates).
I doubt that it would work from the G4 because there's no readable file system on the SL disc as far as the G4's concerned (SL has no PPC support at all).
The combo updater is of no use without the retail installation in the first place.
If the OS is still there on the MBP, just download the combo updater and run it. It won't hurt and it may correct some anomalies. (I don't see why you're involving an external drive for this).
But I rather think the DVD player isn't going to be fixed that way - it would only feature on the combo if a component of the player was changed between 10.6.3 and 10.6.8.
So at base, if the combo doesn't fix it you need somehow to run the 10.6.3 retail DVD. I would suggest an external DVD drive if the DVD drive is broken, but I'm not 100% certain you can install fom there.
Perhaps one of the other contributors can help us there.
The external HD should certainly be put to use to backup your existing system in case of problems. You don't have original discs either, so the current installation is your only source of the iLife applications among others.
That can be done easily using the Restore function in Disk Utility, which will produce a bootable clone.