When you say flashing green light, are you sure. See link for colour of lights.
Did you try a factory reset of the Homehub by pressing a pin into the recess button on the rear for about 20 seconds or was it just a soft reset by pressing the reset button on the rear?
You can still get some of the stats on the Homehub as long as your computer is connected by Ethernet. You do nt need to be connected to the Internet.
Sounds like you have a faulty Homehub. You need to contact BT and report a fault and request a replacement.
Presumably you have checked the cables are not damaged or disconnected.
The home hub 3 will not work on Infinity on its own, unless its connected to an Openreach modem.