I called last weekend and they were supposed to escalate my case, but no one has called yet and it is so bad tonight that our Hughes Net phone won't allow me to make a call to call support. It is our only phone we have no cell service here. I can't even run the speed test it is so bad.
The second one is a web acceleration error; the first one may be reporting something wrong with your setup. Someone else here may have more information about this and may have an idea if there's anything you can do on your side.
The HN staff on this site can run remote diagnostics on your system, but they won't be back until Monday, unfortunately.
I've never seen a 14.1.3 State Code and I can't find any info on it, but judging by those with similar numbers it likely has something to do with device connection, whether via LAN cable or WiFi. If you see it again try to get the description next to it.
If you have another LAN cable you may want to try it in place of the one connecting the ATA to the modem.
The Web Acceleration issue may be temporary.
First and foremost, you should either remove the pictures or edit/crop them to remove the SAN, as the SAN is your account number, which should never be posted in public. You can edit your posts by clicking on the three dots to the upper right of the post and clicking "Edit Reply".
As for the 14.1.3 State Code, it's as I figured, with it indicating some kind of device connectivity issue. With the problems you're experiencing and the State Codes your'e seeing it's definitely something the reps will have to help with. As maratsade mentioned, they'll be back tomorrow, and one should reply then. Make sure to leave your modem plugged in so that the reps can run remote diagnostics on your HughesNet equipment in order to determine the cause of the issue.