I can certainly sense your frustration, looking at the 622 gathering dust for a month! They should have at least hooked you up with one tuner operational through the cable you already have until the rest is resolved!
EDIT - Can't use just one tuner - other one constantly reports "Acquiring Sat Signal"...
The 622 came with a "separator" that takes signals from that single cable and feeds them into the 2 tuner inputs, but that method only works if the other end of that cable is attached to a DPP LNB at the dish or a DPP44 switch in between. That switch is ~$200 from Dish or the installer or possibly cheaper via eBay. Another possible issue is that particular switch has been in short supply recently so the installer may not have had one available.
Depending on what else you have (like 4 orbital slots), your system may need the DPP44 switch in which case Dish will supply it and it should have been on your work order. In most multiple-dish/LNB applications tho' the 34 switch is all that's needed so that's all Dish will provide, but then you'd also have to run the second cable to the 622. If running the second cable is impossible (might be possible via another route?) or impractical, then the 44 switch is a good option, but if your programming does not require it then you would have to pay for it yourself. There may be other options that I haven't considered and others can comment on. Good luck with it and do report back. Welcome, BTW...