What the rules say
The rules state, a tower shield grants total cover if you give up your attacks. Total cover usually obviates the need for a hide check. Successfully hiding (or not) is the result of an opposed check; Spot versus Hide. You make a spot check any time you have a chance to see something and you make a hide check when you want to hide, usually as a part of movement. Obviously, the hide check only matters when someone has a chance of seeing you, though you may or not be aware of others, so your DM may have you roll when it does not matter, to avoid giving you information you would otherwise not have as a player.
Interpretation 1 Invisible Shield
Since you give up your attacks, you gain total cover. Total cover obviates the need for a hide check, so as long as you don't attack, therefore: you are "hidden". There is nothing specific in the tower shield rules about what happens when you move, so since you carry your shield, the cover moves with you. Since there is no facing, this is in all directions and since you are hidden, no one can see your equipment, including the shield. Since being hidden is equivalent to invisible (Rules Compendium), you are effectively invisible and gain the benefits of the invisible condition.
Interpretation 2 (Visible shield and player - The one I think the rules support)
Since hiding is an opposed check, and you can't hide if someone is observing you, there's no opportunity for a hide check (even though, with total cover, it otherwise would be unnecessary).
Interpretation 3 Invisible Shield
You could hide while no one was observing you, then while successfully hidden, move to the battlefield, remaining hidden. However, that's not how I understand hiding works in RAW, but is quite possibly a common understanding.
Hiding in 3.5
Hiding is actually somewhat difficult in 3.5. With respect to sneak attack, often the conditions that enable hiding preclude you from using it. For example, if you wanted to shoot an arrow from hiding, there either needs to be a vision differential (darkvision or low light and bright/shadowy illumination with position/radius in your favor) or cover or concealment that allows you to make a hide check, you but not your opponent. Earlier rules editions had the concept of "back stabbing" and I think this idea has perpetuated with the players, but "sneaking" up on an enemy in 3.5 to use sneak attack is quite difficult. It wasn't even explicitly clear until the Rules Compendium that you could sneak attack purely from a successful hide/spot (because your opponent is flat-footed with respect to you). However, the rules for opponents being flat footed at the start of combat and flanking give alternative (and arguably easier) ways to achieve sneak attack. Some rules expansions helped sneaking in like Moving Between Cover and Sneaking Up From Cover.
How hiding with total cover works
Ignore the tower shield for a moment. If you were behind a wall, with enemies on the other side, you don't need to make a hide check, since you have total cover and they are unable to observe you. If you move around a corner of the wall where opponents might see you; it's no longer possible to hide because in order to make a hide check, you must have cover or concealment and you just removed that by moving from behind the wall. You could use something that otherwise grants you the hide check, but that's not using the wall at that point. If the wall is your only source of cover/concealment or hiding ability, you cannot hide.
In the case of the tower shield, there is no conceivable circumstance where you can make a hide check without some other form of cover or concealment or ability granting a hide check since you may be observed.
The tower shield does not grant "hidden", it grants total cover, and hidden is not a condition or state; it's the result of an opposed check. As such, the other abilities and rules extensions that allow hiding when not in cover and concealment operate as normal, with no other impact from the tower shield (other than the steep armor check penalty).
Facing and line of effect
This does present the question, does the total cover from a tower shield grant total cover in all directions? The rules for the tower shield do not say anything about this, and the common understanding is that since there is no facing in 3.5, yes. The MAIN35FAQ addresses this by making the inference that because the tower shield is providing cover, it must have a location on the battlefield, like any other form of cover or concealment and has direction with respect to line of effect. In my opinion, it's a pretty reasonable inference, but it isn't otherwise mentioned in the rule books.