Yosemite on an Early 2008 iMac 20" with 4GB gives too many beachballs Question

Can you suggest a (series of) test(s) or monitoring that can show what is happening when the system fails, or some test that can show that the harddisk is borked or if some network issue is at hand?

Background

Upgraded from Mountain Lion. For a week or so it was like my box was on steroids, then I saw the beachballs more and more often. Took a backup, formatted my disk and re-installed Yosemite from scratch - no improvement.

Symptoms:


Last two times I started the box, Safari, which I just ran to save a wallpaper is stuck with a great big spinner. Nothing else can be run and even the top bar was missing. When I turned the computer off and on, I was sent to System utilities which made me suspect a harddisk failure is imminent and perhaps the root problem.
I have now let the computer sort itself out - when I woke it, all tabs in Chrome were in a state of loading, but immediately got the pages loaded and I have for now as I write this a very responsive system.
When in Chrome (my default browser, I sometimes get no response, then a beachball, then more often than not an "Aw Snap" or Kill page? which make me suspect a network issue (all other devices are happy with my time capsule - iPhone apple TV and iPad - yes I am 100% Apple here) 


I contacted Apple Support with this story as a Yosemite issue and was told to re-install snowleopard which came with the machine. I want to make sure my iMac is borked first since then I will upgrade to a newer iMac instead.

The fact that I am now breezing along with no issues and pages loading and switching much faster than under Mountain Lion makes me want to first investigate if there is something you guys can detect based on some test you can suggest.



Hardware Overview:

  Model Name:   iMac
  Model Identifier: iMac8,1
  Processor Name:   Intel Core 2 Duo
  Processor Speed:  2,66 GHz
  Number of Processors: 1
  Total Number of Cores:    2
  L2 Cache: 6 MB
  Memory:   4 GB
  Bus Speed:    1,07 GHz
  Boot ROM Version: IM81.00C1.B00
  SMC Version (system): 1.29f1


UPDATE If your iMac slows down and hangs like mine, have a look in the console for hardware issues. An SSD in addition to the 4GB I already had resulted in a fast iMac.
There are a couple of Things you could try:


run "Disk Utilities.app" from /Applications/Utilities and start 'Check Volume' and 'Repair File Permission' there are probably some issues here
start the "Console.app", also found in /Applications/Utilities/ and check for errors while starting
Clear the Caches either by starting the Mac in single User Mode (press and hold the shift-key while starting up) and restart the Machine again. Best would be to run 'Onyx' and clear out the Boot Cache.


Don't forget that spotlight would be reindexing your machine after an upgrade, so that could be an explanation for the slow performance at first.