I believe the only thing you had right was "your new career will not be an installer."
On the serious side.... I'll try and assume what you have, and provide some possibilities.
"Will a dish 500 with the usual 110 and 119 satellites work with a DP34 switch." Yes, provided the LNBF's are not legacy.
It sounds like you have a "SuperDish 105" with a "DP34 switch", connected to a DishPro receiver. (If you have a legacy receiver, then there is a "DP Adaptor" connected between the receiver and the DP34 which will need to remain when making the below changes.
I'll assume this setup is working, but you have rainfade on one or more of the 3 satellites. Therefore, you would like to peak the SuperDish 105 for satellite 105, and use a Dish 500 and peak it for 119 and 110.
I would ensure the DP34 is connected as follows; 119 on Port 1, 110 on Port 2, and 105 on Port 3, and the system is working.
Before you continue....
The DP34 switch will only work with DishPro, DishPro Plus, and SuperDish LNBF's. Therefore, make sure the 2 LNBF's or the 1 Twin LNBF on the Dish 500 has a black
DP on the back. If it does not, you will need to go and buy either 2 DishPro Dual LNBF's, or
1 DishPro Twin LNBF to use the Dish 500.
Now that you have the Dish 500 (with DishPro LNBF) connected to the DP34 switch, set the skew and elevation on the Dish 500 for your location. Then peak the azimuth, and then peak the elevation again, for both the 119 and 110 satellites.
Then peak the SuperDish 105 to receive satellite 105. Since it is working, you should only need to peak the elevation and azimuth for the strongest signal on 105. However, if this does not provide an acceptable signal on 105, and you do not intend to go back using it for 119/110; then you could adjust the skew to 90 (which = +/- 0 degrees), and then peak the elevation and azimuth for the best signal.
EDIT: If you need some more info, how about your ZIP CODE and Receiver MODEL(s). Dish has moved some locals off of 121, but I don't know if they had moved any off of 105. If they did, then you may not need 105, and could just peak the SuperDish 105 to receive 119 and 110; or replace it completely with the Dish 500.