So what you are saying is you have 2 single lnb's, one for each orbital, and there is a switch, but when you run the cable from the switch to the 322, it only picks up 119 correct.
Sounds like you have either a 34 switch or some legacy switch, not a current Dish Pro plus switch.
To answer your question as simply as i can with out knowing all exact products on install...,..
No you cannot run one wire from each lnb and to each sat port on the back of the reciever. It wont work right.
If the switch is a dish pro or earlier type switch you will need to run 2 cables from the switch to the 322, one to each sat port on the reciever.
So yes use the switch, run 2 cables from switch to rec. Should work. Unless the switch went bad.
There are so many variables with installs from the past it is hard to determine exactly how it all needs to be hooked up without you giving descriptions of the equipment, pr posting pictures of the products.
I hope what i did post helps out.