I take pictures with my cellphone. I originally bought a 6 MP camera, got a new phone and it had an 8 MP camera. Needless to say I only carry my phone. lol Every report I can export and picture that I take gets attached to the support ticket for the call for future reference. Most of the pictures usually go into a folder on Dropbox with a link put into the ticket, though (I routinely delete any client pictures older than 6 months from Dropbox).
Anyway, as a person who exclusively uses Linux as their operating system (not dual boot) for the past 8 years, let me tell you: Linux does crash. It is far more fault tolerant than Windows will ever be because it was made for server environments and the entire point of the system is to keep it running as much as possible. You will have a huge set of log files if things start faulting, though.
If it doesn't POST and shows nothing on the screen, it's the power supply. If it POSTs without video, it's the video card. If you still have no video and it doesn't provide a beep code (otherwise, follow what the beep codes say), barebones it, reset the motherboard settings with the jumpers/switches, etc. to try to get it to work. If it works on your bench but not at the client's look for a short.
If you get video and it freezes on boot, it's the mobo. If you barebones it and it POSTs fine, troubleshoot what you disconnected one-by-one. Swapping RAM, resetting BIOS defaults, checking the heatsink, swapping out the CPU, etc. until you get it to POST or not. Most serious mobo/CPU/RAM issues will be readily apparent and you don't need a CD to diagnostics test to tell you it's probably a hardware issue.
I will say, however, that if I suspect that there's any problem with the hard drive I will do a backup of their data (not an image). Most of my work is on-site so I don't have hours to spend on preventative measures when the client isn't complaining of or having solid hard drive problems. But, what I have noticed myself doing lately more and more is checking the SMART data on a lot of the hard drives regardless of the issue.
As far as what to tell the client before their stuff dies completely or while I have it... I never tell my customers exactly what I think a problem is, I give them a range, usually from one extreme to the other. If they're having problems with their system crashing, I will tell them it could be anything from a simple virus that needs to be removed or a problem with the hard drive, mobo, processor, RAM or a combination thereof. (Yes, this usually gives them the deer-caught-in-the-headlights look. lol)
Then I paraphrase what it says in my terms: You brought me a faulty computer that is not working properly. Because it is not working properly and could have a mechanical problem, just turning it on or the diagnosis process itself could further damage the computer and keep it from functioning properly (such as a grinding hard drive).
I always tell them the worst possible scenario but I also tell them that once diagnosed and it looks like the estimated cost for repairs would exceed the cost of the computer's worth, I will let them know (not just do it like some repair shops lol). I have no problem letting my customer know that I don't know what's going on with their computer because you need to have a solid look at what's going on to be able to diagnose it. If they are adamant about a possible diagnosis right there, that's when I tell them the above with the extreme ranges -- because if you don't, I guarantee you that the day you tell them it's a simple virus, half their hardware is fried -- Murphy's Law hates us with a passion. lol
When I call them back to tell them what's wrong with it, they have already been prepared for the worst case scenario. You're either a) confirming it or b) giving them good news. 99% of the time the diagnosis you come up with is far better than the worst case scenario, however, if it is the worst, then you're not going to get the surprised client who thinks you broke it. And, with that 99%, they think you're a super tech because you "saved" their computer when they thought everything could be dead. I don't tell them this stuff to make me look like a hero or something, but to cover my butt... It's just an added benefit.