MacBook – How to diagnose hardware issues on the MacBook Pro 13″ (mid 2010)

I have hit some evil kind of problem with my MacBook Pro 13" (mid 2010). The backstory is as follow:

• I bought the MBP in January.
• Felt 4 GB of RAM memory wasn't enough, so in June, I upgraded to 8 GB.
• From here it went downhill.

After a week may be of using the new RAM (2×4 GB memory modules, purchased through Apple authorized service) I began experiencing some strange behaviors in OS X Snow Leopard (10.6.8). At first it wasn't very often, but Google Chrome seemed to crash quite a lot more than before (crashed tabs, nothing more serious though).
Then Lion came out and I upgraded immediately, hoping that it was a software bug. I did an upgrade over SL, not a clean install. The result was just terrible:

• Tons of crashes on Google Chrome (and by tons I mean that I had stretches of time that almost every click inside the browser resulted an instant crash).
• Other applications quitting unexpectedly. This includes everything I use – Skype, Mail, Finder, games, etc. The error was ACC_BAD_ACCESS or something like this (will correct it when I hit it again, can't remember the exact message).
• Kernel panics almost after every wake up of the notebook (after I put it to sleep in the evening).
• Strange Finder/WindowManager crashes, where I cannot manage any window. Cannot use any application. I can click and switch windows, but I cannot type anything in them. When switching windows, the active application in the Toolbar (the bar where the menu is) doesn't change. E.g. it crashes while using Chrome, then I can switch to Skype, Terminal, TextEdit (if I have started them already), but I cannot type anything in them. This means that I cannot even reboot the machine through the command line. During this, I can press the power button and the Power menu comes up. I choose Restart or Shut down and sometimes the machine seemingly goes to restart/shutdown, goes to the grey screen, but instead of shutting down/restarting, it brings me back to the login screen, like when I do logout/login.

Also I began experiencing strange graphical glitches, which are very strange here is a link to a gallery of screenshots ( blacked out things are private stuff, not part of the bug :))

• The first two images are what I encounter the most – red or yellow artifacts on the screen.
• The third one is a bit different. The artifacts are showing my desktop image.
• They appear on random occasions, mostly in Chrome, because I use it most of the time, but I have encountered this in other apps too (skype, MS Word, Pages..).
• The bug appears to be some kind of a rendering bug, I believe before the Video card, because I am able to do a screenshot of it ( cmd shift 3 )
• I can move my mouse over the glitchy area and it remains glitchy
• If I force it to re-render the area by some means: moving the window, dragging something else over it (e.g. screenshot with cmd+shift+4 to select an area)

I believed that all this was caused by the RAM upgrade, so I went ballistic on the MBP and ran all kinds of memtests I could find. The results were not very encouraging:

• memtest86 found an error on the 2nd pass only
• memtest (the tool which you start in single user) found errors in XOR-ing the memory every time I started it (can't find the exact logs)
• Apple test – no problem found, everything is perfect, birds are singing, the grass is green, etc.

I sent it to repair in the Apple authorized service here. Made sure they knew everything I experienced and most of all that they should test the memory modules to see if there is a problem with them. After a week there, they returned it to me and said that there was no problem with the memory at all. They have been testing it intensively for the whole week and no memory errors or something were found.

After I got home, I just formatted it and made a clean Lion install.
This fixed quite a lot of the problems and it was perfect for the first two days. Then some of the symptoms started coming back, but in a very light form – some random crashes, once or twice a day may be, may be less. The graphical bugs once or twice a day, kernel panic once a week.

But here comes the interesting part – After using it for about a month after that, I started encountering the problems more often than I want to. Also I began experiencing something more fun with the external monitors I use. First one day when I went to the office, I plugged the MBP in and connected the external video connector (miniDP-DVI) and BAM, instead of a normal Login screen I see COLOR NOISE, like when there is no signal on an analog TV set. Then it started doing this most of the times when the screen locked and the screen went dark. This is easily fixable through the monitor by changing the source from DVI to VGA and back (don't know how this is related to the above problems, but it happens now and I am not sure if it is a symptom or just bad miniDP-DVI connector). I believed it was a problem with that single monitor, but it started doing it at home too, where I hadn't had this problem a single time before the last week ( same setup – miniDP-DVI).

I still believe the problem has to do something with either RAM or motherboard/video card, but I don't know how to prove it to the repair service fellas, so they can change it.

Today my bootcamp Windows 7 also started acting weird and crashing all the apps with c00000005 (Bad memory access, access violation, just like the symptom I mentioned above). It started out of nothing, while browsing with IE, because I was too lazy to install FF/Chrome. It started killing my tabs on every page I opened and contained some javascript on it. Then Skype went down and so on.

TL;DR; My MBP started experiencing strange behavior after upgrading RAM.

So now to the question itself – What tools I can use to diagnose the problem? What is the most reliable way to test RAM, Mainboard, Video Card (GPU) ? What do you suggest?

EDIT/UPDATE:

Since there were few questions sent directly to me, I believe it is better to add some more information on the solution of the problem.

• The main problem with crashing and unstable programs was, in fact, caused by bad memory module. After two reinstalls of the OS, clearing firmware settings, etc., I finally managed to persuade the local Apple authorized service to replace the RAM modules which they installed during my first upgrade to 8GB of RAM. The stability problems vanished that very moment.
• The graphic problems, though seems to persist. What I have found out for now is that they are caused by some problems in the video drivers for my specific model. After updating to 10.8 the problems still happens from time to time but instead of getting bright yellow or red, I just see fuzziness in some static places while working, but it is very rare occurrence. So your mileage on this may vary for you, but if possible, upgrade to the latest OS or apply all the updates available. It may fix some of the graphic problems. The interesting part is that I have seen this problem on other MBPros from different years and all of them showed different ways of breaking the image.