Two things may be wrong. With the second possibility usually you don't make it to the login screen, so I kind of doubt that's it, but a corrupt install remains a possibility.
This sort of sounds like a common Unity malfunction. The forums are full of Ubuntu 14.04 users trying, usually in vain, to make Unity work. If it'll let you, and it sounds like you may have to do it from the command prompt, you'll need to install another desktop/ interface. If you're having this amount of trouble with Unity I'm not sure whether to try Gnome or not; it's the most popular alternative.
You can also avoid Unity by installing another flavor of Ubuntu. The only difference is the interface. There is no advantage in terms of learning Ubuntu from the books to using Unity; it doesn't resemble what is in the books on how to use Ubuntu. Try Kubuntu or Xubuntu. There are also prepackaged versions like Zorin, which is free to try but costs $12.50 for full functionality; however, on systems old enough to not even get to square one with unity, the install often hangs. You can install the trial version. I just installed Ubuntu on a slightly older computer with an older processor and onboard graphics; the Zorin install hung, but Unity held up long enough to install the gnome desktop, which of course was the first thing I did.
The reason why Unity doesn't work appears to be incompatible video cards. Much is often made of the drivers, but they don't seem to be the problem. There isn't any particular driver that causes issues nor driver solution that fixes them, and indeed most people who run into this problem can't fix it by changing drivers. It is often suspected of being a video issue, and I was outright getting warnings that my graphics might not be able to do what I was doing so did I want to do it. I found a warning that it is important to make the choice when offered not to use the option that may slow your graphics, or speed up your graphics but slow your computer, or whatever. CPU resource intensive graphics features that you don't need, that might be resolved by a high powered gaming video card but most people running Ubuntu don't have that.
And what is more, gnome with the cairo dock LOOKS far nicer (with the low powered graphics option on Cairo dock). I don't even know how what could have thought of that side-slide thing.
Now, mind you, half the world's video cards seem to be incompatible with Unity. I actually read, within the past week, a blog by an organizational psychologist or something of the sort, thinking that the reason why the Unity desktop is having popularity issues is that it was developed in an isolated laboratory and users weren't consulted, as if they had been they wouldn't care, no matter how terrible Unity actually is. I think the key is the part about an isolated laboratory. They didn't use real world computers and have no clue that Unity doesn't work on them; rest of world of course didn't take long to discover that.
You could with Ubuntu 12 or 13 and see if you get the same problem; I believe they are both missing Unity. I myself was able to log in, though my system would only stay usable for about 15 minutes. And I had to constantly log out and do stuff in command line to get the graphics back.
Reading between the lines, you had another OS, or more than one OS, installed on this hard drive, and you wiped it and installed Ubuntu?
The boot loader may be confused. When this sort of thing happens to me I simply repeat the install, and I've never had it not clear up.
Also, now, it's only been a week since I last installed Ubuntu... I'm pretty sure I did have to install it twice, it had Windows... but do pay close attention and make sure that if it gives you the option, and it probably does, you do start completely fresh with a new boot loader, boot partition, everything, I mean, delete ALL the partitions that may have been there. And if that's the first time you've tried that you might get to repeat it yet again.
That's been my experience, the last two times I've installed Ubuntu. One had Windows installed on it and the other had two Linux OS's.