Hey, owners of this "little" beauty.
I have watched this yesterday that was telling of the dangers of leaving Xbox's time capacitor unattended for too long.
tl;dr
* If you have Xbox version below 1.6, you can safely remove the capacitor, however if your Xbox is 1.6 or higher the Xbox will not function without the capacitor, so you would need to replace it instead. An easy way to see if your Xbox is 1.6 or not is to check the manufacturing date on the sticking underneath the Xbox. If it's before 2004 then it's OK, if not, it's probably 1.6.
* Xbox time capacitor, as in the thing that keeps your time rolling while Xbox is off, is prone to leaking
* The leakage can cause corrosion and ultimately motherboard failure of the Xbox
* The capacitor can be safely removed from the motherboard without affecting any functionality aside from internal clock resetting every time you power the thing off
* It doesn't matter whether the Xbox is unplugged or turned off
So, I went and dug out my old Xbox from the closet, phew it was dusty. I opened it up, checked the capacitor in question and lo and behold the little munchkin was all puffed up and going sort of browny in places (I should have taken a picture). I took it out and there was a little bit of leakage just below it which I cleaned up afterwards. I turned it on again and it seemed to be working fine.
The moral of the story is, if you want to keep your Xbox in working order, you better remove or replace the time capacitor as those particular ones tend to blow up!
Hopefully someone will find this info useful.
What's the revision number of my Xbox!?
http://www.informit.com/articles/article.aspx?p=367210&seqNum=2

I have watched this yesterday that was telling of the dangers of leaving Xbox's time capacitor unattended for too long.
tl;dr
* If you have Xbox version below 1.6, you can safely remove the capacitor, however if your Xbox is 1.6 or higher the Xbox will not function without the capacitor, so you would need to replace it instead. An easy way to see if your Xbox is 1.6 or not is to check the manufacturing date on the sticking underneath the Xbox. If it's before 2004 then it's OK, if not, it's probably 1.6.
* Xbox time capacitor, as in the thing that keeps your time rolling while Xbox is off, is prone to leaking
* The leakage can cause corrosion and ultimately motherboard failure of the Xbox
* The capacitor can be safely removed from the motherboard without affecting any functionality aside from internal clock resetting every time you power the thing off
* It doesn't matter whether the Xbox is unplugged or turned off
So, I went and dug out my old Xbox from the closet, phew it was dusty. I opened it up, checked the capacitor in question and lo and behold the little munchkin was all puffed up and going sort of browny in places (I should have taken a picture). I took it out and there was a little bit of leakage just below it which I cleaned up afterwards. I turned it on again and it seemed to be working fine.
The moral of the story is, if you want to keep your Xbox in working order, you better remove or replace the time capacitor as those particular ones tend to blow up!
Hopefully someone will find this info useful.
What's the revision number of my Xbox!?
http://www.informit.com/articles/article.aspx?p=367210&seqNum=2
You can use one final check to verify the Xbox revision that you own (or are considering buying): Look at the BIOS kernel version and dashboard version numbers. To view these numbers, boot the Xbox in dashboard mode (by powering up without a disc in the DVD-ROM drive). Go to Settings and then System Info. A disclaimer will scroll down and will eventually show you two version numbers: a K: value for the kernel and a D: value for the dashboard. You can perform an unscientific check of the revision using Table 3.5.
Xbox Revision 1.0 - Kernel version 3944,4034,4036,4627
Xbox Revision 1.1 - Kernel version 4817,4972
Xbox Revision 1.2 - 1.5 - Kernel version 5101,5713
Xbox Revision 1.6 - Kernel version 5838