Honeywell keypad without power, replaced transformer, control board is getting 120v but no 24v output, no fuse on the board (Rheem AC/Heat Unit)... any ideas

Board unless a safety device is open.

If you have 120 volts going to the transformer and do not have 24 volts coming out of the transformer, either you 120 volts is not hot or your transformer is bad.
If you have a volt meter check between line 1 and line 2, it should be 120 volts.
Check between secondary 1 and secondary 2 you should have 24 volts.
If those two things check out OK then check on the low voltage terminals of you Circuit board. Check between the R terminal and C or Com. Terminal, you should have 24 volts.
In all of this testing make sure that you door switch is depressed if you have one.

Most furnaces under five years old have a fuse somewhere on the circuit board. It is a spade clip type fuse like an automobile fuse.

I found out that the transformer was not getting 120v because the On/Off wall switch broke on the inside which made the Black wire (Hot) loose. How did it break? I don't know... So I bought a new switch and everything is OK. Thanks for everyone who replied.