Welcome to the forum
Would you mind sharing the name of the program with us? Or is it one you wrote yourself?
Most programs need to be installed
AFTER disabling your Antivirus or Antispyware Virus or Personal Firewall security software. Otherwise, those security programs will block certain parts of the program from being uninstalled as the security program sees it as a threat to your Windows environment. Doing this will often fix this problem. Repeat the program uninstall using Control Panel->Programs and Features and power off your computer for 5 min. Reboot and see if the .exe file is now gone. If it is, your problem is solved!
If not, you'll need to take more aggressive actions such as testing your hardware...