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.
I too have been a "techy" and a Hughes subscriber for about 12 years and it has for the most part performed well.
Anything however can "break".
The modem retains extensive logs of its condition, both past and present.
The Hughes employees here in the Community are very well versed in this area, have greater knowledge and experience and have all of the technical resources of Hughes at their command.
They are however few in number and they as corporate employees work 9 to 5 ish M-F eastern time so are working through the weekend accumulation of posts.
They will however see your topic and respond as soon as they can.
Just to expedite things it would help if you could post a case number from a phone support episode or the serial number of your modem that can be found on the bottom or rear of your Hughes modem.
Remember not to post your SAN (starts with DSS) or other personally identifiable information such as email and so forth.
That will ensure that the Mods can ID your account details in the event that your Community log in info does not ID you.