First off it will only take 4 gigs most likely with those specs. An upgrade to 2 gigs or 4 gigs would be nice but most likely not help your issue. What os if Vista or 7 yes get 4 gigs if Windows XP 2 gigs would be fine. Have you tried reloading you laptop this is a quite old one a reload now and then does wonders for older computers. Might want to run some canned air through it to get all the dust out heat could be causing the stuttering too. One more thing to look at is the drive itself.. You have an external DVD drive to test?
1. RAM will help if you're not talking hi-def stuff. If you're running anything newer than WinXP and/or have ANYTHING running at the same time, yes, you are running out of RAM. So picking up a 4GB set of RAM for your laptop will certainly make it run better, period.
2. Clean-up - If you've not defragged your hard drive or run any clean-up on temp files, etc, then that would be a big help as well. For this, I'd suggest: CCleaner and Auslogics Disk Defrag.
3. What app are you using to play your CDs and DVDs? You may come out better using something different. I would try VLC Media Player and/or the KMedia Player
4. Startup Items - You can use CCleaner for some of this - You likely have startup items it would pay to kill-off / disable. You can do this via Start-Run-type msconfig and press <Enter>,.. or you can use CCleaner - Tools - Startup - simply uncheck items there..
5. Registry Clean-up may help as well - CClenaer also does an excellent job at this..
6. If you're talking Hi-Def content on the video side, then your system is going to have a hard time with any of that, regardless of what you do.
7. Should also check for any virus/malware infections - malwarebytes antimalware, superantispyware both work well - what AV are you using? I'd recommend MS Security Essentials or Avira Antivir first... there are some other good ones as well.
8. All of the software I mentioned can be quickly and VERY easily downloaded and installed from http://ninite.com
In regards to the CPU - yes, it is a little old, however it should have zero problems with regular audio CDs nor regular Video DVDs... Hi-Def is another issue, but probably don't have to worry about that from DVDs.
Another thought I didn't think of with my first post.. Try using an external CD/DVD player/burner if you can - it could be the optical drive itself is going/gone bad.. And along those lines, it wouldn't hurt to use a CD/DVD lens cleaner if you have it... not sure I'd go out and buy one, though they are cheap.
And another thought... your performance settings... you could try something as simple as setting your system to max performance settings, whatever they are named on your given system (power settings - usually, with a laptop, just click the battery next to your system clock, and choose from there..."