if you cannot connect to xbox live but can connect to the internet after your system could not download the new update here are the steps you need to take. (more notably step 2 for those who have tried everything already!)
step1: troubleshoot everything on xbox-more notably to delete everything off your hard drive completely, then clear all your system caches on your storage devices. then in the storage screen press LB RB X LB RB X and click yes to delete any updates. and try connecting again via a straight connect to your modem if possible.
If this does not work. as it prob will not follow step 2!
step 2- call xbox live support for a console repair, they should cover this if you explain that the download has caused a fatally corrupt error in your console itself. (the way you can show this is by getting another xbox and testing it on your internet, and testing both hard drives with both x box consoles. record your findings on all variations)
it will be time consuming but should you do this you will be able to find out if your console is only corrupt and fixable or fatally corrupt by the update and therefore able to be resolved by a repair that will be covered by xbox for their mistake with the update.
i would not wait for the new update in 17 days as you will only be able to download it via usb or burned disc and may not repair the fatally corrupt console.
I hope my troubles can shed some light on someone else's and make your path to fixing this much faster then my own as i have spent over 26 hours and 3 days working on this issue over the phone, online, through my internet provider, and personally.