|You do not need to buy anything else.|
"Both printers are connected via individual USB cables (not on a hub) to the computer,"
This is the clue. They are independent of the other. Forget about the working one and trouble shoot the non-working on. Set it as default first in control panel then try test print from printer page.
Did it ever work? Is it new or old? Do you have the factory drivers and applications for it in Window 7?
"The era of big government is over," said Clinton 1996