Have you tried raising the DSL router up higher in the existing location....
Regarding the use of the other phone jack - possibly yes.
Depends on the overall house telephone wiring and the condition of the desired phone jack.
First plug in a telephone to see if the phone jack works. If not look inside the jack to see if all of the wires are connected and secure.
If so, then you can unplug the DSL connection from the current jack and move it all to the desired jack.
Remember that the DSL line has a splitter serving a telephone and the router.
There may be installation instructions and diagrams that came with your DSL cable modem.
Follow all of the wiring as best you can to see where it leads and what is connected. Sketch out and lable all the existing hookups. Take a photographs even.
Move the router and see if it works. If not, move it back. Do not change or move anything else.
You may also need to reset the router so be sure to write down the current settings. Make sure you have admin rights.
If doing any of the above is uncomfortable for you then try to find someone knowledgeable to help. Failing that you should probably contact your ISP.