If the cart is showing on the lcd on the printer, then yeah, run a power cleaning or two and that should get the ink running.
If not, you may need to reset the chip on the cart.
Switching inks without purging out the lines is typically a no-no. Not all of those inks get along when mixed together and you may have congealed ink goo stuck in the lines or worse yet, clogging the nozzles on the head. It might be prudent to throw a cart full of cleaning solution in there and run the power cleans and then put your new cart in and run more power cleanings. This is going to wast a lot of ink and rack up the print count on your waste tank but may be necessary.
Good luck!