I own a '98 Infiniti QX4 and purchased a new keyless entry remote for it. I have been told that the sequence to program it is to lock the doors, insert the ignition key ten times, wait for lights to flash, and press unlock on the remote. However, I have been unsuccessful in my attempts. How can I get it to work?

You are missing one step. When you see the lights flash after inserting the key numerous times, you must insert the key one more time and turn it to the ON position. Then you press the unlock on the remote. You will see the lights flash one more time as you press unlock button on the remote. Take the key out, unlock the doors and try the remote. It should work fine.