I would still use the system, yes there will be things to keep an eye on, but without using it, we could miss a clue as to what may be behind this, the worst cases are when there is multiple issues, those are really hard to figure out from a distance.
Now assuming the system temperature is stable, and under say 50 degree's (way hotter than I like), we can try changing the ram about if you want, but no matter what slot we use with any stick of ram, always put that stick back on it's original placement that it is currently in, the notes take care of any moving, but the sticks must be kept in order so if 1 is failing, then it can be isolated.
The colour slots are important in their way, systems can have the ability of dual or Tri (triple) channel, Tri channel is not as common as dual channel, but these features mean they work together and provide the best performance, and they should be bought in matched sets, as they have been tested as working together without issue, but to use these features, they must be placed in the correct slots on the board, that's where the colours come in, as it's more obvious which are the ones to use.
For testing none of that comes into play, what we are testing for is a single stick, and\or slot, that is showing signs of trouble, so if you are ready to start, remember the procedure for safety I laid out previously, more so with touching ram, it doesn't take much static to cause problems.
To remove a stick of ram, open the locking leavers at each end of the stick to be removed (1 at each end of each slot), they "fold" away from the ram, have a look at the free slots, move those ones to get an idea of what I mean, you will need to apply a bit of force possibly, but don't go crazy, that's why I said look at the free slots to see what I mean.
So counting stick 1 as closest to the heatsink, remove stick 2 and 3, and place them accordingly on the paper you have marked up, and with stick 1 left in place, fire the system up and see how it goes, it will be slower to work as you only have a single stick now, but it's stability we are looking for, well instability really, if it's stable it suggests there is nothing wrong, which is the ideal.
But run that and use it for a while, more so if you can do the same thing as what it takes to set off any crashing you experienced previously, if all seems well move that stick into slot 2, and repeat, then slot 3 and repeat, you see the pattern lol 
Now repeat that again with just Stick 2, then with just Stick 3, remember you need to do the same sort of things as when the problems were occurring, if you get any issue note what stick, and what slot were being used when that problem occurs.
You will need to run it like you would before when you were crashing, and give it a good chance to show out each time, if you only do it for say 30 minutes, it may not be enough to see if it has any problems, once they have each had a good turn, let us know how it went, also if it crashes, also take note of the system temperature using SpeedFan (linked previously ^) or something, as that could also be the problem, so keep an eye on both, and see how it goes, then we can go from there.
*edit
Forgot to cover putting the ram into slots, there is a notch in each stick of ram, there is a corresponding lug inside the slot, these MUST line up, so the sticks can only go in 1 way, trying to fit it the wrong way round could break the ram, or even the slot\board depending how much force is used.
So if you keep the ram in the same direction as it came out of the slot, it will help, now when you insert the ram into a slot, make sure it's the right way, insert it into the slot, get both ends into place, then apply an even downward force on the stick, it should click into place, and the locking lever should rise up and lock home.
You may hear them click into place, then check the locking levers are fully up by lifting\pushing them into the ram (the reverse of undoing them), if you get the system bleeping after doing a change around, it means the stick is probably not inserted right, so you will need to check it is properly inserted and secure, "IF" it still does it, and no other stick, or slot does, that may be the problem piece, but give it a go, and let us know how it goes.