A problem connecting to the gateway would only affect the transmit and receive LEDs.
A router to modem cable connection would only affect the top LAN LED.
Having all five LED's ... I would first check, if you haven't already, make sure that the DIN connector on the rear of the modem is pushed in ALL the way.
It goes in rather far and on some modems is very hard to seat completely.
Just to clarify, that will be the connector with the red circle around it:
Also be sure the coax cable is firmly tightened.
Beyond that the forum Mods will have to run remote diagnostics on your system to see what error codes are set.
That really is about all you can do on your end.
I'm sure the Mods will be along shortly although this is Monday and they will be working on the weekend backlog of posts so please be patient.
Frankly after having posted here in the Community I would skip the phone support at this time.
The Hughes employees here are at the corporate level and are VERY good.
They will see this post and reply,
They will also run remote diagnostics from their end to look at the modems internal logs.
They can if warranted send out a replacement modem or handle a tech visit if that is required.
They will respond as soon as they can and they WILL get your issue resolved.