Aside from the fact that it's Time Locked, shouldn't the Doctor (pre-Time War) have noticed the lack of Time Lords/Gallifrey/Daleks/Skaro during his travels in the future? The modern Doctors have been treated with shock whenever he reveals he is a Time Lord, and many species believe them to be a myth. Why did this never happen to previous Doctors?
The Doctor did not notice any odd before the Time Lock was put in place because there was nothing odd to notice.
Before the Time War happened, had you traveled into the year 5 billion, odds are good you could go visit Gallifrey and see a Time Lord. Any sufficiently advanced time- or space-faring species would likely recognize a Time Lord (though they might be surprised to see one outside of their home world, as that kind of travel seemed rare for the Time Lords.)
One the Time War happened, all of those Time Lords were impressed into the army to fight the Daleks. Every Dalek and Time Lord to ever exist in the entire history of the universe (with a few notable exceptions) was fighting the Time War when the Time Lock went up. They were removed from spacetime completely at that point, and no longer had ever existed.
Thus, the memory of and consequences of the events and actions they took pre-Time War still existed, so beings with sufficiently long lives, memories or oral/written histories would know who the Time Lords were. But there would never physically be any; it would be as if they had gone extinct before any given species recorded history began (though that would not be entirely accurate, it's about the best any other species would likely be able to comprehend). Thus, seeing one in person would be a complete shock. Even species high-order enough to grasp the idea of a Time Lock and understand its function would still assume all the Time Lords were locked up, and not expect to find any wandering free.
You might have also asked why the Doctor didn't know much about how to get back to his Tardis in Blink. Time, he suggests famously, is timey-wimey and wibbily-wobbly. Until an event becomes fixed, it may not have occurred, but once it does, it affects things around it. Strax, for example, visibly changes after Jenny's death, because his past is being rewritten in real time. Vastra, aware of the fixed nature of the event and able to reconcile the atone paradox is not, and the event has become fixed, leaving her unaffected.
The Daleks are not immune to this rewrite either, having forgotten who the Doctor is during the course of the Asylum (the one where Clara is first introduced).
The events of "The Name of the Doctor" (namely that a Time Lord must not visit his own grave) and "Fires of Pompeii" (differentiating between fixed and unfixed points in history) seem to suggest that even though the Doctor can travel through history, there is significant danger in traveling through one's own history. The Doctor is clear with Donna that certain events are fixed, and that he just "sees" which ones are (like the volcano) and which ones aren't (like saving a Roman Peter Capaldi from it). What he sees and what he chooses not to see are based on that. The facts that have been established in history are formed at the moment he knows of them, so it is in his interest not to learn about certain things, in order to keep them from being established.
The Five Doctors echoes this, as the entire premise is based on a time scoop that brings them together, but it too takes an enormous amount of energy.
Very early on (The Aztecs) it is established that you cannot change history. Barbara attempts to save a young man who is to be sacrificed. When saved, he gets angry at Barbara, at the indignity of being denied the ability to be sacrificed, and kills himself.
Also, Fathers's Day highlights the perils of forcibly trying to change the timeline. The Doctor is clear that there would be significant danger in meeting themselves and especially in Rose touching herself. The creatures that clean up time paradoxes are nasty.
These all add up to a situation that leads Time Lords to avoid knowing their own timelines or fixing events in it. Finding Trenzalor, for example, is so bad the Tardis won't go.
Additionally, it is established in canon (most recently in the Children in Need episode, Five and Ten) that when a Doctor meets himself, the earlier incarnation will forget most of the encounter. The best Ten can do is suggest to Five that he learn particular skills. As such, even if a later version of himself were to tell an earlier version of the Time War, he would most likely forget about it. But he also would have the habit and training not to look for it in the first place, remaining blissfully unaware of what he is about to do.