It is said that the internet remembers all. That is true in some cases.
If you happen to have the original URLs to the website (or any website of interest), you may be able to find some of the information that you were looking for.
The Wayback Machine as it is aptly named, can be a handy resource when looking for things posted on the internet from the past. When you enter in a URL, it will display a timeline and you can click on the marks to see what the page looked like at that time when it was captured. There is no assurance that the links on the page displayed will go to a saved snapshot of the page you want to go to, but sometimes it does.
Still images are more likely to be there, but links to videos may not get you a video that you seek, especially if it was a link to another site like YouTube.
I hope this helps and Good Luck with your search!