If you do not hear the tilt/trim motor running, then first check your fuses. Not sure which fuse controls the tilt/trim on that engine, but in the back of your owners manual there is an electrical schematic that should show you which fuse.
On the side of your engine, there will be a tilt/trim switch. With your key switch turned on, see if that activates the T/T mechanism. If so, then you have a wiring problem between the engine and your controls. If not, then do the following.
The following is based on my 225, but I think your 90 will be the same. Facing the rear of the engine, on the left side, you should see a large slotted screw that is the manual relief valve. It will be near where the engine bracket locks onto your transom. Open it up about 1.5 to 2 full turns. Then tilt the engine up all the way. (I use a come-a-long mounted to a beam in my garage and a piece of tow strap to do this.) On the right side of the engine, you will see a manual lock-up brace. Turn it down so the engine is in locked up position.
Check the hydraulic fluid in the T/T holding tank. It should be full. If not, top it off. If it needs a lot of fluid, you have a major leak in the hydraulic system which you will need to track down. But your T/T motor should still run.
If hydraulic fluid is ok, then find the T/T motor where the wire come out of the top. Follow those wires until you find the connector. Disconnect and put a volt meter on the prongs coming from the engine. Turn on your key switch and try to activate the T/T. You should read 12 volts +/-. If so, then you likely will need to replace your T/T motor. If you are mechanically inclined, you can do that yourself. Otherwise, take it to a dealer or Honda certified tech. If you do not get 12 volts, then you have a problem between the connector and the T/T relay.
Let us know what you find.