The difficulty in watching YouTube combined with the difficulty in completing a download of the latest Flash player together imply a network problem. Maybe your ISP has issues, or maybe your own connection has a problem. Check your modem parameters and see if the line is running at full speed, if you have any tools that allow that.
I had some trouble with my line a few weeks ago with symptoms very similar to yours. A bad connection may continually drop individual sessions and may function at extremely slow speed, producing problems with anything that requires high data rates. If it doesn't clear up in a few days, or if you see indications of problems with the line (abnormally low connection speeds for the DSL or cable modem, noise on a voice line, etc.), contact your provider.