Okay Bob, I probably made my last response too wordy, giving you a lot of information that you don't need. Here's the simplified version:
You don't have to power-cycle your keypads to check the addresses, only to program a new address in a KP.
If you have 4 keypads total, then your keypad addresses are most likely to be between 16 and 20. 16 may or may not be in use, but it's available. If 20 is not in use by another KP, then it may not be enabled.
Press 1 and 3 simultaneously until it beeps, on your other keypads to check their addresses. If one of your other keypads has the address "16", then the highest address of any of your keypads will probably be 19.
The 6150 Keypad you replaced is unlikely to have an address of 16--that address is usually taken by an Alphanumeric keypad. See what address isn't taken by the other 3 keypads, and try that for your replacement keypad.
If 16 isn't used by one of the other 3 KPs, then I would use that for your replacement address, because it's always enabled. If 16 is used by another KP, then you will probably need to use 17, 18, or 19, whichever is available.
When you're ready to try to to program your new KP again, get a buddy to work with you to power up from the panel. DON'T use a wire at the KP to power up.
I understand your reasoning for "needing" to power up with a live wire at the keypad. Here's my reasoning: When you power up by connecting a live 12VDC wire at the keypad, it sometimes zaps the keypad. Sometimes you get away with it, other times you don't---like running a red light, even for the best of reasons.
As a last resort, if you can't get a buddy to help, then use a long extension cord to plug in the transformer and plug the cord in near your keypad.
If your replacement keypad isn't responsive to KP address programming like your other keypads, then you may already have zapped it. Let me know how it goes.
EDIT: And no, you aren't becoming a pain in the butt. I sometimes forget that not everybody is used to working with hundreds of scrambled wires and I sometimes make my answers more complicated than they need to be.
I'm afraid I won't buy the "old and not too bright" syndrome, although I'm retired myself and I sometimes pull the age card. But anybody can get confused when you're working with something you're not familiar with.