I don't understand the thinking here, as Madman says you need RAM, but if the RAM is not through the roof as you are accomplishing those tasks then the slowness is not the RAM? But from your description it very well could be the RAM with enough high ram usage programs open. Swapping out the distro ain't going to help anything in theory if you are not Overusing the RAM. I just hate to see folks wasting time and drive life swapping out operating systems when the operating system is not the issue.
That's old hardware and will only do so much. That being said, it's not bad hardware and should run decent. You should test things one at a time so you know the RAM is not the issue. Then ask yourself if they are acceptable running one at a time. Also, Mate should run well on that pc. I've been using Mint's Xfce lately due to issues with Mint Mate, and it will be perfect for old machines like this.
Open the System Monitor and set it to be on top and watch it while you are running these programs.
Also, What things are you using all at the same time? If you are careful 4GB will work fine but admittedly is a little limited.
All that being said, you should check the HDD for errors. That's the first thing that goes on any computer, and this computer is getting old. If that is the original HDD, there is a good chance that is had some bad sectors etc., hopefully not.
I'm running an Intel Core i5 2520M on a laptop now, and it's not all that fast either.