Ouch.  Sounds like you could wail!

I don’t have any brilliant ideas, just some process of elimination stuff.  A few areas of concern are:  Improper embouchure, mechanical problems with the sax or bad reed.  In all of this, I am assuming that you are using a good reed.....not the one that you used when you used-to play the sax.  If you aren’t using a new reed, please buy yourself an inexpensive plastic one (2.0 or 2.5 strength). In the US we can get them for $7 - $10, sold individually.  They don’t sound perfect, but they are very consistent.  If you are using a good natural fiber reed, make sure you soak it in water for 5 minutes and use it for 5 or 10 minutes before testing any horns.

1) Find another woodwind player and have them try out your horn and set-up (Reed and mountpiece).  Another sax player would be ideal, but most experienced woodwind players should be able to get a decent sound out of your sax if it works.  See if they have the same problem as you do.  If they don’t, your problem is very possibly your embouchure.  Sounds like you were pretty young and talented when you had a teacher last.....perhaps it was your talent and not the teacher who got you to the level you were at.  You may have also had embouchure instruction that didn’t work for your mouth. 

2) Find a music store somewhere.  Take your mouthpiece with you and try out one of their alto saxophones. See if you have the same problem.  If you don’t have the same problem, your sax might need a tune up. 

3). Find a music store somewhere.  Take your sax and reed with you and try out some alternative mouthpieces.   If you don’t have the same problem, your mouthpiece has problems.

4). Check your reed strength.  If you used a 4.0 reed in the past, dial it back to 2 - 2.5.  You definitely need to re-grow your embouchure muscles before you can handle a hard reed again.

5). Consider that what caused your problems a few years back, may not be what is causing you problems today.

6). Repair technicians have varying capability.  I have a local guy with 30 years experience who checked out my horn and said it was all tuned up....yet I had problems playing it.  I took it to someone out of town who said it was a mess.  I invested $800 into an overhaul, and voila - the horn is amazing.....leaks, poorly mounted pads....all sorts of stuff were wrong with it.

7). Remember, you don’t have an embouchure any more.  You might need to play for a month or two before you can get the low and high notes out.

Last note:  You mentioned “All of the keys seem to be strong enough”.  That is an unusual statement.  You shouldn’t have to push down very hard on the keys to get them to seal properly.  The keys shouldn’t have to be strong - just aligned.  If you find yourself having to push down hard on the keys to get good notes, you definitely need your horn repadded and the keys realigned.

Good Luck!