Sudden loss of air on tubless tyre, and now it won't inflate Finding bike answers on the internet is really hard when you have no idea what you're looking for, so I'm sorry if I'm asking a ridiculous question here.

Cycling back today I went over a bump in the pavement and heard a noise come from my front tubeless tyre. Sure enough when I got off and felt the front it was quite deflated. Upon getting back home I've checked the tyre over and can't find any punctures. I then tried to reinflate it (a presta valve, which I have unscrewed and attached my floor pump to) but the valve won't take any air. When I get a proper seal and pump the air appears to go in but I think I feel it escaping from where the valve stem joins to the rim.

I'm suspecting that the valve might be busted over the bump, but I'm not sure how you can tell. Is it possible to just replace the valve in this case?

I've looked a lot around inflating tubeless tyres from scratch and the general feeling I'm getting is that it's very difficult, you should generally use a compressor. Is this the same for reinflating tyres you are not reseating? And how would I tell if the valve is dead or if I just can't get enough air behind it?

Also the valve is entirely depressible into the wheel frame (pretty much). Is that normal in the case of there being no pressure?

This is a bike I got from the shop with the intention of learning more about it as I go, and I guess here we are learning about it.

Thanks in advance
Your valve should NOT be depressible into the rim.  You should have a presta ring screwed in it, else nothing is retaining the valve and your air probably leaks from there!

If its not the case, if the tyre is seated correctly on your rim, inflating it with a pump should be easy.  Maybe you have a dent on your rim where your air is leaking.  

Yes absolutely, you can get a new valve for tubeless tire.

A good way to find where your air is leaking from is spraying soapy water around and check if an area makes bubbles.  It will tell you exaclty where your leak is from. 

Cheers