Well...it doesn't sound promising...BUT....
Before "going in", I would disconnect the the lower shift rod from the upper and see if shifting it directly, using JUST the lower rod, will make it engage. What you do is apply either upward pressure (for forward gear) or downward pressure (reverse) while slowly rotating the prop. If all is right inside the gear case, it should slide fairly easily into gear using this method. If it doesn't then you WILL need to go in and take a look.
While doing this little "exercise" make a mark or two with a felt tip pen on the lower shaft so that you can accurately measure the amount of travel it goes through when shifting from one and then the other gear.
After you have your measurements, move the shift lever on the outboard just as if you were still hooked up and compare the amount of travel the UPPER rod goes through. If the upper rod's movement is shorter than the lower rod....there may be a problem up top. If the travel of both rods is fairly equal in distance then my prediction is that your clutch dogs are worn and the gearcase is "bound up". If the clutch dogs are worn, the hand selection of gears is possible because you are rotating the prop by hand. The fact that the transmission will go into gear like this is a GOOD thing even though you will need to go in and replace the clutch. It is not at all hard to do. But may be above some folks "pay grade".
The clutch dogs get worn naturally...over time....with regular use. It is the case with ALL clutches that wear takes place. We just have to deal with it. ;~(
BUT...and it is a BIG BUT....the clutch can be PREMATURELY worn out by "soft shifting". An outboard should be placed into gear with a crisp...BANG sort of movement of the shift lever. If an operator S.L.O.W.L.Y. pushes or pulls the lever... ...in a soft, lackadaisical way.... and a sort of chattering or ratcheting sound can be heard from the transmission.....THAT is the sound of the clutch dog faces bouncing off of each other. It is also the sound of early clutch failure. So...if you...or your partner... have been "soft shifting"....time to do it the hard way.
But you'll need to replace the clutch first.
But Hey! It's a 2002 and it could just be what happens after 12+years. Below is the parts diagram. The clutch consists of both bevel gears...Items #5 and 6...along with item #1.
You CANNOT just replace item #1 and have it work correctly. The clutch consists of ALL the "squared" off pieces of #1 and those that are part of the gears. I have also tried to file the ledges of the "dogs" square again after they have been rounded off from "bouncing. I'm here to tell you it doesn't work. What filing them square does is change the dimensions and keeps them from "clicking" together.
http://www.boats.net/parts/search/H...BF5A2 LA/PROPELLER SHAFT PROPELLER/parts.html
If you're lucky....you may find the pin that holds the spring sheared or the spring itself is broken....if the clutch dogs or "ears" aren't too badly rounded off....then replace the pin...spring...or both and you're back in business cheap. But if it IS the clutch....$170 + shipping ain't too bad to get your little sweetie back.
Good luck.