Raspberry Pi B+ RaspMBC random reboots

[Smallwater]

I have a Raspberry Pi model B+, and I use it with RaspMBC to use it as a media centre. It worked flawless in the beginning (4 days ago), but lately it suffers from random reboots.
I've got 2 external Hard drives, hooked up to a hub, all three of those powered on their own. The USB from the hub is the only USB connected to the Raspi. I am then connected to my TV using HDMI, with CEC enabled. Lastly I have a standard patch cable connected for my network.

I've read in other posts it can be caused by either too low power input, but I've tried with different chargers, including a standard Samsung charger which delivers 2A at 5V. I have no access to a multimeter however, so I haven't been able to measure the voltage on the board itself. I do however, have it plugged in a power strip, along with lots of other things (about 10 things - a lot, I know).
Other posts inform me that overclocking could be the cause, but I am not doing this. At least, not to my knowledge.
I also read that it could be caused by low memory, but I have no idea how that could happen. I use it in a normal fashion, just to watch movies or series, and nothing more. When I enable debugging, I can see that there is no drastic lowering of my free memory or increase in CPU.

The reboots happen at random times, but I've noted some patterns. It only reboots when I'm watching a clip in 1080p. Smaller videos play without trouble.

I have tried to reinstall it, with success, but the reboots continue. For no reason at all, suddenly it just shuts down and starts up again. I've already enabled dirty rendering.

I can understand that I can be the umpteenth noob that asks this question, but any help you can give will be much appreciated.

EDIT: Posted the log files as well. I can find nothing of note in it.

[elatllat]

Try removing the usb and see if it still reboots, try other things to narrow options down

[Smallwater]

I have tried many things. When I enabled dirty rendering, it no longer crashes when idling. I also noted that it can play non-HD quality videos without issue, the reboots occur only when I play 1080p videos.
I'm getting a new charger this day, I'm going to try that.
Is there any way to know if there is something broken on the board itself, without the use of a multimeter?

[elatllat]

I have tried many things...

1)
rpi crashes when I play any 1080p.
from any freshly installed OS; raspbmc, openelec, raspbian, Arch, etc.
nothing on usb.
the sdcards passed a corruption test.

If that's true then you might still have a power issue like a crappy usb cable or dirty mains power, to rule that out
2)
same sdcard works in another pi.
same 2A psu and cable works in another pi.

If you cross all that off and you have not overvolted then maybe you can get a RMA.

[Smallwater]

So far, it only crashes when playing 1080p files. On first boot, it takes about 30 minutes before crashing, but after that it only takes 10 minutes, or sometimes even 3.
I have tried 2 different SD cards, both freshly installed and not corrupted (checked on laptop, Windows 8.1).

The PSU I use now, I borrowed from a friend who used it on his rpi, with no issues.

My best guess is that the GPU doesn't get enough power, but I have no way of checking that, as I don't have a multimeter.

I'm giving up. I'm calling the merchant where I bought it on Monday, and I'm going to ask for a replacement.