SOLVED AT LAST!!
My problem with not getting any signal at all when I upgraded to the newest firmware was an HDCP issue. The Xbox wasn't getting an HDCP handshake from the TV and so it wouldn't boot at all.
I did some research online and it seems that is an issue that many other Xbox users were having with TVs of many brands. The only variable in the equation was the HDMI cable itself, so I replaced my old cable and everything is working perfectly!
I suspect my old cable wasn't HDMI 1.3 compliant, thus it didn't take the handshake from the TV. My new cable IS 1.3 compliant, and it gets a handshake no problem.
Thanks so much to Jim and Toshiba for all of the support! Now to watch some Netflix...