This is exactly the type of situation warranties are designed to be invoked on.
Also, they will probably know if you opened the case, despite Linux711's trivialization of that point. Many systems have "case intrusion" detection. Wether they use it, I don't know. It might not even be a condition of the warranty, but it usually is. (And no, I haven't a clue how the mechanism works, either).
So, if you fiddle about inside it, you <might> find out what is wrong, but chances are, there is a faulty component inside; which would need to be replaced. So you would either replace it yourself (which depending on the terms of the warranty may void it) or you would end up sending it back anyways and they might discover that the case has been opened and send it back to you untouched.
So the terms of purchase include not opening your case to say add extra memory or a new graphics card? Do you see where your logic is falling off the wayside?
It's not so much his logic as the way most warranties work, and with good reason. What if somebody purchases a new computer, and then installs new memory or a graphics card, and a failing in one of those new components causes the motherboard to be fried? Or they replace the power supply and wire it up incorrectly? Surely failing of another manufacturer's components or the possible incompetence of the tinkerer (not you, that was of course a hypothetical example) isn't the liability of the computer manufacturer?
I really don't know if they use the case open detection thing, but I would imagine they do; after all no doubt it would be shipped in a "closed" position, and opening opening the case would flip it, so the techs on the other end will know that it was opened, which may cause problems down the road if you do need the warranty after all. While it is possible it is merely a loose power connection to the motherboard -although that seems doubtful to me, they are generally quite secure- there is also a good chance it is a faulty component (such as a power supply, the motherboard itself- even RAM or any add-on cards that came installed)) At which point you might not be able to use their (Acer's) warranty services as they might simply send it back to you (because it was opened). Then your only recourse might be to seek warranty replacement from the actual manufacturer of the faulty component, but unfortunately you often don't get a manufacturer warranty from OEM components in prefabricated machines.
TL,DR version:
There is a good chance opening the machine now
could cause more aggravation and possibly cost more down the road then an uncovered shipping insurance charge would now.
of course, all that said, if I was in the exact same situation I would probably open it up, even knowing the above risks. Also because I don't learn from previous experience, having been bitten by everything I've said before and even being in the situation you are putting your friend end and voiding other peoples warranties, a fact which they firmly believe to be my fault to this day...
In any case, since you are planning to go ahead and open it anyway, most of this post was unnecessary vitriol.
If it was a faulty component the computer would at least turn on, hum, flicker or do something wouldn't it?
Not necessarily. I've had bad RAM prevent a computer from turning on at all. a bad power supply would certainly do it as well. a bad motherboard too.
The only time I've heard of a new cpu flat out not turning on is when my friend has bought custom pcs and some things weren't plugged in all the way. Is this most likely the case?
It's certainly possible, but I don't think it's the most likely scenario. It certainly would be the best case scenario, and the one to hope for when you crack it open. The rigors of shipping could have loosened one of the necessary power connections or an absent minded engineer didn't connect it to begin with.