I seems to be OK. Just a few software glitches(errors) caused by the failed battery.

From where the video left off, what you'd normally do there is:

First try to shut it down by holding down"Control+Alt+ Delete" keys together and hopefully the "Shut Down" dialogue should appear. (allowing you to shut it down) Then start it again. (it may take a few reboots before it becomes stable).

If you can't shut down as described above the you should do what's called a "hard reset".

To do that you hold down the on/off power button for up to 10 or more seconds or till it shuts down.
(This suspends all activities"reading and writing to the HD etc." before it switches it off)

(TIP: You should never disconnect it from the power while it's running as this can cause "errors" on the HD(Hard Disk)).

Then start it again

If you have any questions just ask. I'll be only too glad to help if I can.