The 1st thing you have to do is try to determine if it’s merely a software issue with your OS install or if the problem relies on the hardware (whether it’s the screen or the computer itself).
In order to facilitate that task, you must check the obvious.
1) The DVI adapter (already tested).
2) The Screen. Can you hook the monitor to another computer?
3) Can you hook another monitor to the same computer?
Extras: Have you tried another VGA cable?
The above should result in any of the following:
a) The screen is defective, change screen.
b) The Mac mini has a hardware issue where no other screen works. Time for repairs (probably not worth).
c) The Cable is defective, change cable.
d) The screen works fine on another computer, the Mac mini works fine with another display. what…?
In case of D, there could be a problem with the software instead, either the driver that the Mac mini is using when it detects the display is broken or the video driver or something. That’s a whole new world and -as already suggested- you might want to try booting from the install CD/DVD and trying to see if video works there. Back up your drive and a full reinstall might also help you have everything fresh.
Hope it helps. I know it’s a lot of obvious steps, but this is how the tech guys do it :) Find the problem first.
UPDATE:
After reading that the Mac mini doesn’t work with a different screen and that this issue happens before login screen (i.e. it’s not ‘user’ related), there are two possible ideas you can try before a complete OS reinstall.
You mention that it works in Single User but not safe mode; given that Single User goes straight to the command line, have you tried running fsck on the partition? Maybe there’s some data corruption in the OS X volume.
Safe Mode doesn’t load external drivers and items in the StartupFolders, so that should work and I find it weird that it doesn’t. Of course make sure you unplug all external devices (sans keyboard/mouse/display) before diagnosing a problem like this.
In any case, I’d try to install a fresh copy of OS X on an external drive (if you don’t want to wipe your internal copy) and see what happens from there. If the external copy works, then the OS X copy has a big problem. I know this is obvious (and it’s already in your list of things to do) but sadly debugging a problem like this without access to the OS/hardware is really hard. You can always later clone the freshly installed OS X to your internal drive to avoid the reinstall in the internal drive.
Good Luck!
Your trip the Genius bar was too focused in my opinion. I suggest you make another appointment and lay out your case above, but this time, don't mention the memory tests, but that the problems showed up when you upgraded the RAM. Refer them to your old case number (tack this visit on as a follow-up).
Tell the Genius on hand that the problems still exist and that they need to do further testing. As it stands, your Mac is unusable. Additionally, tell them to make note that you have tried a fresh re-installation and it did nothing to help (don't mention that things ran fine for a day or too, stick to the current state of the system), which will rule out any software problems.
Ask them on what they suggest and follow it (no matter how annoying it may be). If it doesn't fix it, call them and do another follow-up. If they tested the RAM and it passes, then it might be the logicboard.
In any case, do not visit them with "the solution." Let them find it through there own testing. Clearly, the logs containing kernel panics and all the problems you list will support your case. Moreover, their internal testing tools are much more sophisticated than what you'll scrounge up on the net through 3rd party apps (they actually have in-house diagnostic utilities for these occasions).
I would highly recommend that you stop spending your time diagnosing the problem and let them do it for you. That's what they're there for.
If after everything is said and done, and they still can't pinpoint a problem, you will likely walk away with a new Mac. Just focus on the problems you are suffering from and leave the diagnostics to the Geniuses and technicians.
You may want to downgrade back to the 4 GB for now. And it's of note that replacing the RAM and the hard drive yourself do not void your warranty for that particular Mac model.
PS: You don't specify if you took your notebook to an Apple Store and spoke with a Genius or some Apple authorized repair centre. I would strongly encourage you to deal with Apple directly. They'll not only treat you better, but likely solve the problem with less headache. My advice is tailored to them; you are totally on your own should you choose a 3rd party repair shop. To galvanize the need to deal with Apple, let me put forth the following. I had a friend who purchased a Mac mini. There were strange problems during boot up where it would occasionally load the keyboard set-up assistant. The machine was also sluggish and exhibited other unusual anomalies in its day to day. We took it into an Apple Store and the Genius tried to reproduce the errors. He couldn't. He also expressly stated that minis never required repair or servicing. But with all that, he elected to replace the entire unit and gave my friend a new mini. Took it back to his place and it hummed, no more issues. I doubt he would have received the same treatment from a computer store authorized to service Macs. Deal with Apple direct; I cannot stress that enough.
Best Answer
I like to just do speed tests as you adjust the antenna when I don’t have a software defined radio and/or oscilloscope to measure the actual signals.
I’ve not seen any good tool that uses the compass or just shows that weak a signal since the noise is so large compared to the signal.
So, no - you’ll need to try them sequentially and also sight things visually or do even more measurements.
Hopefully someone has a better guide to field test, it’s so changeable based on hardware I try to do anything else but use that anymore. It was great when ATT and iPhone original came out, but after a while it’s needing a PHD to decipher.