So I have received my new P4 today and when I plugged the battery in to charge, it didn't do anything. The lights didn't change for over an hour.

Then I thought I'd press once, then press again and hold to turn it on like you would if it were in the drone.

Now it seems to be discharging the battery...

Is this normal?

Just read up in the battery booklet and I have turned it off. It stated not to turn it on during charging.

However, the P3 batteries showed the charging lights to let you know it is charging and it's amount. This does not happen with the P4.

Maybe I'll leave it for a few hours and see if it charges properly.

LED's should be blinking while charging -> Read the manual

That's not the case, it should light up to show the current charge of the battery as it's charging.  
Snip from the manual

User Manual

There is an intersting note above about powering on if above 95%, however, there seems to be yet another contradiction in the documentation.  This really is terrible for such a big time company.

This is from the battery guide in which the OP was refering to;

Battery Guide

Doesn't anyone proof read the documentation?  Do you or don't you power it on ever, at all, about 95%???????   DJI you really need to check the documentation, you are dealing with potential accidents here by not providing the correct information.  

The 95% trick was the same with the P3. I guess the battery has to be turned on to fully charge if the battery is at 95% or above otherwise it wont charge.