Okay I have  the   Eyelander, Ali Baba's Wee Booties and  Splendid Screen.    What I assume is all I need to play a melee focused demoman.   It obviously must be user error because I can't for the life of me get into a groove with this setup.     Am I completely wrong to think to try to play the demo this way?

Well, yes and no. If you want to play a successful melee only demo you really need the full demoknight set. The best way I've been able to remain consistent with the demoknight set is to know when to back off, when to swing the sword AFTER hitting someone with the charge, and making specific attacks based on opposing classes. Going after a heavy is usually a bad idea, I've found it's best to test the waters and see how they react before engaging them over and over. If they are quick to notice they're being targeted chances are you won't be able to get in enough swings before they finish you off. If they have a medic, don't even bother. Stay away from pyros - they are the hard counter to demoknights. Airblasting will completely shut you down. Spies are very easy targets, especially once you master the timing of your swing right as your shield makes contact. Just be aggressive towards classes that you can out-damage in an ambush scenario. Soldiers are easy pickings if they're not completely ready with a shotgun. Medics are great targets even if you only get a charge in because it'll knock them away from their patient and make them panic.

     It works, but with the Eyelander you have to change the way you play a bit since you can't get health back like you can with the other Demo swords. On the bright side, for each kill you get in a life you get heads which increase your speed. I have a friend that said he had built up to borderline Scout speed. Use that speed to back out of a fight and grab a Med-Kit if you need to (Knowing the locations of those is a generally good thing to know as well). Also, when you charge in make sure to aim for where it seems like they are going, even with the boots your control is very limited. You also need to be surprisingly close to hit with melee, but if you get it at the end of the charge they are pretty much as good as dead.
      You may also want to consider the Charge N' Targe, while you may not be able to deal the same charge damage, you can resist more of it thanks to higher fire and explosive resistance. Same goes for the swords, if you happen to have others mess around with them and get a feel for what you like. While sometimes harder, melee Demo is completely viable as a class build. You just need to overall be more aware and be willing to pull out, after all, there can only be one. 
     Keep in mind that this is just the way I think of it, I'd recommend following dudeglove's advice as well and check out the wiki for more info.

Playing a Demoknight is all about the time from when someone sees you until the time you charge them, and the time it takes you to charge up to them. 
 
Like ColumnBreaker said, you need the full set to use a Demoknight well, but it seems you have that. However, the Persian Persuader is a REALLY good sword, and goes with the other two items in the set really well. Just learn to innately know when to charge and when not to. If an enemy sees you before you charge, if they're far enough away, they'll recognize how to get out of the way in about a second. If they (and their teammates!) don't see you, and you think you can aim the charge, kill them, AND be able to get away, go for it.  
 
You'll die a lot at first; it'll take a bit for your to realize how much his limits are. But don't be afraid to ambush people; with the new set, it's possible to kill a group of up to 5 people if you pull it off correctly (don't see you before charge, charge isn't extremely long, and keep getting kills so you get health from their dropped metal). Don't be afraid to charge if it's "not that far"; with the Splendid Screen, you'll get some good damage off no matter how far you charge. Just make sure that the shield gets to hit before you cancel the charge by swinging. 
 
Knowing when to back off and when to charge in is the main crux of Demoknight. As you play, you'll get better at knowing your limits; just act on those and you'll be able to get MVP (trust me, I've done it, it's possible).

The best way to play demoknight is with a frying pan as your weapon.

DON'T! Demoknights are dicks!

I don't think I have the eyelander yet, but I've got a sword and shield, and had one of my best kill streaks ever at the end of Upward.
 
it's all about location.  If you can squeeze behind enemy lines and patrol their ambush points, you can do some real damage.  Tight short hallways and stairs.  No open areas, obviously.

I think the Half-Zatoichi is better than the Persian Persuader when playing Demoknight, to be honest. You lose the 6 second cooldown on charge, but instantly being at full health every time you kill an enemy and random crits are far more useful, I find.