Chrome has its own build of Flash so I recommend trying that. Also, try firing up a YouTube video and letting the light gray bar go all the way through first. Try playing then since it will already buffered the whole video. If it does fine your Internet is the problem.
Since you are complaining the whole machine is slow, are you talking about beach balls? Try doing disk copies (large files to and from) and make sure it doesn't randomly hang or slow down. Now it is sounding like a hard drive cable if thats the case.