Hey Jfamily,

A couple things. Are your batteries new? even though they show to charge they could have dead cells and not enough umph. to kick the big motor over, They may have enough to trim it down or up and then would be spent.
If you tried switching to a battery that is absolutely positively good and you have the same issue, I would check for corrosion around the wires on the battery and the block.
so
1st things first/ Verify you have 2 good batteries (they can go bad sitting over the winter) Take them to Advance or another parts store and they can check them for dead cells. Charge them all the way up before you go.
2nd check for Dirty cable connectors at the batter and where the positive cable hooks to the starter and the negative hooks to the block of the engine.
3rd If these two things do not correct your issue, then check for blown fuses at or around you engine. These may be at or around the Key Cylinder or at the engine. You could also have an inline Relay or Fuse box that needs to be reset by pushing the reset button (kinda like a ground fault outlet in your house's bathroom or kitchen)
4th If none Detected, or one thing starts working and not the other, check for Solenoids that could be bad as part of the Tilt/Trim. Depending on the engine, these could be on the engine ot on the Trim Pump itself. A quick google search should tell you.
I hope this helps... Good Fishing!!