Assistance with Kenmore 90 Series Dryer

My dryer began shutting off after running for a short time. If I hit the start switch immediately after the dryer shut off I would hear a humming noise for a brief period, but that was all that would happen. If I let the dryer cool, it would start up again. After a few days of this, the dryer would no longer start even when cool. I took the dryer apart and found that it was full of lint. The motor had a thick layer of lint all over it. I cleaned the lint as much as possible and was able to get most of it clean. I then checked as many of the circuits as I could find. All of them had continuity. The control board looked to be in good condition. I put the dryer back together and tried to start it. It fired right up and ran for about 15 minutes. I noticed it made much more noise than before and made progressively more noise as it ran. I finally decided to replace the motor. I notice that the replacement motor is not the same part number as the original, but it looks pretty much identical and appears to install the same way; however, now that I have a new motor installed, the machine refuses to start up. I can hear the timer moving, but the dryer doesn’t make any other sound when I hit the start switch. Are there any steps to installing the motor that I may have overlooked. I did replace the 3 prong power cord with a 4 prong, but I believe it is installed correctly and shouldn’t be an issue.

Any assistance would be greatly appreciated. Thank you in advance.