Missing Flash plugin all of a sudden

It's a 2008 regular MacBook (sorry I can't get more specific than that, but it is the black colored one, which I believe they only made for awhile), and I'm running OS X Version 10.5.8. If it helps any further, I'm running Safari 5.0.6 (I don't believe this is the current version, but when I go to update it, it says it's up to date).

Okay so I uninstalled Flash, and now I keep going back to install it (but this time for my version of OS X). And just as what has been happening, when I go to download it, absolutely nothing happens. I click on the "Download Now" button, and it takes me to the page that says "Thank you. Your download will start immediately and may take a few minutes to complete (etc., etc,)", however nothing downloads. I open the "Downloads" window and there's nothing in it. So it's as if Safari is blocking Flash from even downloading.

Okay I reinstalled Safari, restarted, checked to see if the Flash plugin is installed (which it isn't), then went to install the Flash player from Adobe's website, and just has been happening, it won't download at all. I click the "Download Now" button, it goes to the next page, but absolutely nothing happens. I open up the "Downloads" window, and it shows nothing is downloading. So you could sort of say my problem is Flash simply won't download when I try to download it from Safari.

Okay I did all that, but when I tried to download Flash from Safari, it wouldn't download.

I should mention that I tried downloading Flash from Firefox, and it downloaded perfectly, however Safari and Firefox are still indicating there's a missing Flash plug-in, even though it is in the Internet Plug-ins folder in the Library.

UPDATE: So I was finally able to download Flash from Safari. However, since then, I've uninstalled/reinstanlled it several times now, yet I'm still getting a missing plugin message. While some YouTube videos actually do work, the others don't, and homestarrunner.com, which is pure Flash, doesn't work at all. This is also despite the fact the Flash plugin is in the "Internet Plug-Ins" in the Library (there's a "Flash Player.plugin" file along with a "flashplayer.xpt" file).
So it now simply seems like Safari (and Firefox) aren't recognizing the Flash plugin. Any more help would on how to fix this would be appreciated.

All I have in the Internet Plug-ins folder is Flash Player.plugin and flashplayer.xpt, and there are no duplicates, so as far as I know I only have one version of Flash player (and it's 10.3 because I have Safari version 5.0.6, so it's not the newest version of Flash. I tried downloading the newest version just to see what would happen, but it would quit unexpectedly every time I tried to open it).

Sorry for the late reply, but YES THIS WORKED! THANKS!

However, now I'm having this problem in which Safari will unexpectedly quit and there will be no error message after it does so. It mostly does it when I have 2 different YouTube videos opened up in 2 different taps, and Safari usually crashes when I start to play the second video I loaded. But now, it's beginning to happen at random (usually after I've been using Safari for awhile). What could be causing this? It just started happening ever since I downloaded that file Klaus1 sent me. Could that possibly have anything to do with it?

Before my Flash stopped working, I could overload the Tab Bar with YouTube videos (over 12 at a time) without Safari ever crashing; especially the way it is now (without any warning and with no error message popping up after it crashes). It's also crashing almost at random now; even while I'm watching a YouTube video and I have no other tabs open. In fact, I've never had Safari crash like this ever in my five years of owning this MacBook until after I downloaded that Flash "trick" file, so I don't think it could have anything to do with my RAM, bandwidth, or cache size. Any other ideas of what it could be? Again, this just started happening.