Got my nice new HT-1R today, plugged it in, only to find it does not work.

It turns on, but there is no sound. It does make a pop sound as its turned on and off.
I'm new to Tube amps so I Don't really know about common problems with them.

Any ideas why this is?

Check the tubes are seated properly. Pull them out and plug them back in again.
Gilchrist custom
Yamaha SBG500
Randall RM100 & RM20
Marshall JTM45 clone
Marshall JCM900 4102 (modded)
Marshall 18W clone
Fender 5F1 Champ clone
Atomic Amplifire
Marshall 1960A
Boss GT-100

Cathbard Amplification
My band
I've never used that amp, does it have a standby switch next to the power switch? Most tube amps have a standby switch, they are so you can turn the power on and let the tubes warm up, then you turn the standby switch on and can play.
Godin Icon Type 2 Classic
Vox SDC 33
Mesa Boogie Express 5:50 2x12
Roland Cube 80XL
Boss Tuner
BBE Boosta Grande
Ibanez TS9 Tube Screamer
Amptweaker Tightmetal
ISP Decimator
Zoom G3
TC Electronic Flashback
Visual Sound H2O
video was a bit jerky and quick so I couldn't really tell what you were doing. Make sure the guitar volume is up and cable is in correctly. Otherwise, I'd say you got a borked one and you need to exercise your warranty/return policy.