Anyone ever watch the Japanese movie Rashomon? It's a story about a samurai who is found dead in the forest, and the authorities question the few people who were witness to it. The flashback shows the samurai and his wife were traveling along a road when a lone bandit manages to tie up the samurai and proceeds to rape the wife. But then there are three different accounts of what happened next.
In the bandit's version of the story, the wife pleads that the bandit and the samurai duel, to spare her of the guilt of having known two men. The bandit releases the samurai, gives him a sword, and the two of them fight honorably and skillfully. In the end, the bandit gains the upper-hand and slays the samurai, but the wife runs away after her husband's death.
In the wife's version of the story, the bandit flees from the scene after raping her. The wife begs the samurai for forgiveness, but he merely glares at her, not moving an inch. She quickly cuts him loose with a knife and asks that he kill her to rid her of her shame, but again he does nothing but glare. Eventually, the look her husband gives her drives her so insane that she murders him with the knife and faints.
The authorities manage to call upon the dead samurai himself via a spirit medium, and in his version of the story, the bandit asked the wife to go away with him. She agrees, but only if the bandit would kill her husband to ease her of her guilt. The bandit is put off by this sudden request and rejects her. She runs off, and the bandit frees the samurai on his own. The samurai is so overcome with grief from all that had happened that he takes a dagger and kills himself.
There is then a surprise fourth testimony from a secret witness. After the wife was raped, the bandit asked the wife to go away with him, but she instead releases her husband and leaves it up to the men to decide who she stays with. At first they do not wish to do so, but after the wife prods and mocks them deliriously, the engage in a rather pathetic fight to which the bandit is the victor out of sheer luck. The wife flees in horror when the samurai is killed, and the bandit runs off with the valuables alone. The witness had apparently come across the scene while looking for wood, but had kept his story secret because he himself had stolen the dagger from the scene before reporting to the police about the body.
Although there are four different accounts of how the samurai died, the fact remains that at one point the samurai was slain. There is one set truth, one set past and one true way that this happened (which in likeliness is that of the fourth witness' story), but we as mere humans may not be able to determine what it is. Regardless of our ability to remember it, however, the true events did happen.
Therefore, the past does exist in this sense.
However, there is a slightly more controversial point that could be brought up in the favor of people who believe that the past does not exist. You see, the past is time before the present. Time is a conceptual method of measuring duration and intervals, but it does not actually physically exist. People and objects exist as matter/solids/gases, lights and sounds exist as particles and waves, even ideas and emotions exist as chemical and electrical pulses within the brain. But does time itself exist? Only as an idea, a concept. The present is an idea/knowledge of the world around you at currently. Time past then is a memory of that. Please note that I'm using the word idea loosely here.
You're looking at your screen, and the the knowledge, the idea, of the present is entered into the brain. However, once it's been entered, it becomes a memory. More knowledge and ideas can be derived from this memory, but it is a memory none-the-less. If the past is time before the present, and time is an idea that becomes a memory the instant after recognition, then past ideas do not exist. Only memories of them.
To sum up, you can remember time past, but it does exist anymore. It did exist, but it does not exist now.
I applaud anyone who was brave enough to read through all of that. <.<