Online videos play choppy. It's getting worse, and I don't know how to fix it.

Sorry it has taken me so long to get back to you.  I hope this information helps as my problem is not getting any better.

This site has the specs for my computer.

Please note that I have 1gb of RAM installed, which is not what it came with.
http://h10025.www1.hp.com/ewfrf/wc/document?lc=en&cc=us&docname=c00280659&dlc=en#N1119

It's a relatively old computer; Slow hard drive, slow processor, outdated videochip and slow RAM.

Flash is probably never going to run very well again unless you turn down the graphics all the way. This can be achieved by right-clicking in the Flash application and changing the quality of the video.

If your entire Windows installation is slow you might want to consider a re-installation if it hasn't been done in a few years. Could net you a performance gain. Make back-ups before you do so, though.

Your computer has an AGP slot for a video card.  If you want to continue using that computer for awhile, I highly recommend installing an AGP card to replace the onboard video you're currently using.  AGP cards are getting harder to find.  If you're in the U.S., here's one I will suggest: http://www.newegg.com/Product/Product.aspx?Item=N82E16814139028.  But, also determine the output of your power supply first.  This card only requires a 250 Watt power supply, so you might be OK there.

Yeah, your onboard graphics are likely the biggest limitation in your comp. Here is a link to all of your options for a new graphics card: http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=100007709%20600007850&IsNodeId=1&name=AGP%204X%2f8X

If you decide to buy one, post here first.

It never did this before

It wouldn't hurt to reinstall OS after backing up all documents before purchasing a dedicated card.

Hello starbreeze!! I'm brand new to this forum and I'm just reading some of the posts here. I have a fair knowledge of the puter.
You have been given some excellent advise by several members here on the forum.
I have a computer club in a retirement center where I try to help seniors with their PC's.
I just found this forum and I'm very impressed with the helpful answers given on this post and other post that I have read.
It ain't easy to reformat and start over, but it would also be my suggestion before speeding money on more hard ware.
It seems you have an old rig. A fresh start of your OS will help. Be sure you make a back up things you don't want to loose.
You will need a external USB for that. If you have never started with a fresh OS, it's a good learning experience. It sounds like you have the knowledge to do that. If not, I'm sure there is some one here that can help. God luck friend!!
garybear!!