Both earlier today, and about an hour ago, I upgraded to OS 10.10.1 on both of my Macs, and things went well. What happened in both cases is that after selecting restart, the installation proceeded (said it would take 7 minutes, but took less). At the end, the machine re-booted by itself, and then a screen appeared, asking (via an unchecked box) about sending information to Apple regarding some "things" (can't honestly remember what it said, as I left the box unchecked). I clicked Continue, and the desktop appeared, like normal.
After that initial installation, both machines were somewhat slow in re-starting up, but as I said, it went well. Now, they start up like normal.
For your issue, I'm wondering when you turned your machine off. If you did it during that re-load process (after the 7 minute installation completed), that could cause issues.
When you used Disk Utility, did you 1) Verify and Repair Permissions, and 2) verify and Repair the disk? If you did, and are still having issues, and without having access to a more robust disk repair program like Disk Warrior or Tech Tool Pro, another possible "solution" is to re-install OS 10.10 "over" what you have now. Not sure how that will go, and also what will happen (if anything) to the applications you have. Maybe some other folks have another solution.
It's unfortunate that you do not have a backup. On these forums, I am seeing that so, so often! Yet, it is rather painless to do. In fact, one can use the "free" mode of SuperDuper! to make a bootable backup (preferably to an external device). I always make such a backup (actually two copies) for both of my machines as part of my maintenance/backup processing every Saturday. I know this does not help you now, but once you get your issue resolved, I strongly suggest you start doing that. If you had done that, you could boot your machine from that bootable backup, and do a restore from it to your internal drive.
Additionally, one should do disk maintenance some what frequently, so that the machine runs fine. Again, this does not take much time. One excellent tool I use (and it's free!) is Onyx. I have been using for such a long time, that I depend on it (along with Tech Tool Pro and SuperDuper!). It has had a number of excellent reviews.