While I don't run windows 10, I do run norton and while it is a memory hog It should not slow down the computer to the point it's useless especially if all your doing is web browsing and watching youtube videos, not enough to notice a large difference anyways, on startup yes it does effect the performance.
ccleaner and a defrag and reboot your modem may help you a bit, If it were me I would wipe the laptop and start fresh. I would recommend this if your upgrading your OS anyways. If it didn't clear up the issue then maybe norton is to blame, but I seriously doubt it.
I can run several websites at once with videos and music on a dell inspiron laptop with an i3 and 4gb ram.
not a computer tech, just a suggestion.
+1 on matador's suggestion your system specs would help
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