Most units (of which I am familiar) bring 12v from the battery to the center wire of the Up-Down switch. then one of the Single Pole Double Throw (SPDT) other terminals (3) delivers that voltage to one of 2 solenoids (relays) which are wired to apply the voltage to the tilt motor in opposite directions.....like up is +/- and down is -/+ to the motor terminals.
I'd go to the switch, verify 12v to the switch and then measuring at each outer terminal, move the switch to the UP-DOWN positions and see that the voltage follows. If not....new switch....ebay has SPDT switches for a song......generic device. If so, check wire to UP solenoid for 12v at the solenoid when UP is pressed. If that's gook, go to the OHMS scale on your meter and check the ground terminal for the solenoid to have contact back to battery - usually through a contact on the engine block proper. Then check to see that the power/ground wires to the motor from the UP relay are intact. Since you have a new solenoid, somewhere along the line you should have discovered the smoking gun.
You didn't say what solenoid you used as your replacement. If the same OEM part number then disregard the following. If not: The solenoid is an electric switch using a low current control circuitry to operate a high current switch (really....daaaaaaa).
It has the high current set of contacts but needs the low current control circuitry to operate. The low current circuit has to have both sides of the battery across it. Some relays are like the ones used (used to be used) in your automobile and had 2 ⅜" stud, high current terminals and either 1 or 2 low current (control) terminals for activation. The ones with only 1 terminal, are internally wired to the bracket and through the bracket they get the - return to the battery.....with a bi-directional motor requirement where both polarities change to change direction you won't be using the single control type solenoid/relay.
Other relays are in a rectangular, plastic encased housing with pins that plug into a socket, and others have exposed terminals that are soldered to the connected wiring. Commonality of parts says that both would be the same part number/type......just a little bit of info if you need it fine, if not so be it.
Well it's 4:20 and I'm getting sleepy so I think I'll go back to bed and maybe back to sleep.