Your laptop is undersized. Put the maximum RAM you could fit in there. Google your model to find out. Most likely you can fit 2gb of RAM in there. Change you resolution lower, to something like 600x800. The less pixels it has to control the less it has to work & consume resources. On the lower setting your icons, apps, & text might look too big, but there are settings in Windows to just make them smaller at the lower resolution. You can also set the display settings down to 16 bit 800x600 if you don't mind a slightly less than perfect picture.
You OS isn't compatible with modern flash & players. Get windows XP or Windows 7 in it. Sometimes you can get old dead computers to get the OS & license off of it. You can also use a light free Linux OS like Lubuntu or Xubuntu. A 2012 version should work well in the older machine.
Your internet speed or incompatible flash player may not be fast enough. With downloadhelper or other video downloaders, you can download & save the video rather than watch the video, then just play it back later. Your VLC media player will then play the video. With VLC, you can play the video when it's only downloaded halfway, while the rest of the video continues to download, so you usually don't have wait for the entire video to download.
You will have half the video already loaded as a nice large buffer, & completely get around the buggy & resource hungry flash player.
If you go to Windows 7, go to services & disable all services you don't need or your machine can't use well to streamline the OS. With Linux, don't install any more apps & crap than you really need.
My 1.8ghz single core AMD laptop from 2005 with 768mb (0.768gb) of RAM played movies up to 720p fine running XP, Windows 7, & Xubuntu. But now I'm up to 1.5gb of RAM on it to speed other things up on it. You will not be able to get it to play 1080p video though because your laptop cannot be fitted with a good video card, & wouldn't be compatible with modern ones anyway.
An SSD (solid state drive) will also boost performance, but that machine won't support it & SSD TRIM properly. With the massive amount of file-swap required for the SSD, it would probably wear out in a few months or year. That older machine may only have a 4200rpm drive in it. By upgrading to a 5200rpm drive you'll have a significant performance boost. The RPMs may not be much faster, but the newer 5200rpm drive has more data per square inch on the platter than those old 4200rpm ones. So you're almost doubling drive access speeds. Also the newer drive has a bigger cache at 8mb or higher for better performance, were the old 4200 one may not have any cache at all or utilize some of the RAM as cache.
Also avoid drives above 500gb. Drives below 500gb tend to have only a single platter with lots of data per square inch for fast access. The larger drives are multiple platters, less data per inch, so slower to access.
You can also go to a 7200rpm drive, but in most cases the difference between a 5200rpm & 7200rpm one may be barely noticeable, where the difference in a 4200rpm & 5200rmp drive will be very significant. So save a few bucks if you have to with a 5200rpm one.
That old machine may be a PATA (also called IDE) drive. So make sure you don't get a modern SATA drive, because it won't work.