Bear with me here
Ok so the basics are - due to the side effects Desmond's 1996 consciousness became unstuck in time and travelled to 2004. His 2004 consciousness however, was suppressed, and his 1996 mindset remained, hence why he had no clue what was going on.
Now, is it possible that when Desmond found his constant, his two consciousness synchronised? As Rocco (I think) said in another thread, Des seemed to be filled with an optimistic sense of purpose after leaving Penny's house. Also, as we saw in the 2x01 flashbacks and 2x23/24 flashbacks, Desmond seems to be a optimistic character (pre-Island/hatch). Is this because he was filled with an unexplainable sense of purpose? In 1996 (after finding his constant in 2004) he doesn't consciously acknowledge becoming unstuck in time, because finding his constant allowed his mind to make sense of things, to differentiate between the two times. Therefore, his memories of travelling forward in time to 2004 were suppressed, much like his 2004 consciousness was suppressed when the side effects took place.
This is a bit of a stab I know, but I've been trying since Thursday to make any sort of sense to all this