What you can try to test the system to see if it works at all is to raise the motor manually. USE EXTREME CAUTION !! Two people are usually necessary and a good way to lock the motor in the up position. Most outboards have a locking device on the stern bracket. You will have to open the "manual release valve" on the trim unit before attempting to raise the outboard. They are usually accessed through the side of one of the stern brackets.
Once the outboard is raised and secured, fill trim unit with proper "trim fluid", replace cap, close the manual release valve and run the trim up and down a little (with outboard still locked in the up position). Refill the unit and repeat as necessary. You may have to wait between refills for any air bubbles to dissipate as hyd fluid tends to foam up when re-filling a "dry system". Once there is enough fluid in the unit to start activating the rams, safely unlock and lower the outboard. Run trim down fully and let it sit for 10 minutes or so for the bubbles to dissipate. Then run it up as far as it will go. It probably won't go all the way up since it will still be low on fluid so you repeat the above procedure.
This should make the trim work if everything else is OK. It will also expose the leak(s).