Uno only works when serial monitor is open

Got a brand new Uno, uploaded a sketch that was already working on a different Arduino on to it. I then switched the two Arduinos out & it didn't work. I checked connections & switched boards again to be sure it wasn't hooked up wrong, it wasn't. I then went back to basics & tried just a simple blink sketch & the new Uno worked for that. I then reconnected it, checked & rechecked the wiring & it still didn't work properly. Just as a fluke I discovered that things worked fine if I opened the serial monitor. As soon as I close the serial monitor it quits. The sketch only includes the serial code for troubleshooting, it's not needed otherwise. The sketch is meant to work via external power. What am I doing wrong?

Some questions: Are the arduino (hardware) versions the same? Is the UNO a SMD? Could you post the output of when you hold the shift key & press the upload button (the one that is not working)? What do you mean by "it quits". How can you tell? What do you have connected to the arduino? Detail matter, the more the better. Take a close look the UNO board anything look different/weird? Post pictures.

Yeah, I guess I didn't want to get too annoying & provide too much detail so sorry for what I left out. For your 1st question no, ones an Uno (with R2 in fine print) the other is a duemilenova. No it isn't a SMD. I will have to post the output as soon as I can but cannot right at this moment.Your right, "It quits" is vague, when I close the serial monitor what is supposed to happen changes. I'll go into detail here in order to try & explain. The Uno has a motor shield connected to it, this is the one sold by NKC electronics not the Adafruit version. there are two analog inputs in the form of 5k ohm potentiometers, one switch, & one infrared detector - digital inputs, one led as output & a motor as output off of the motor shield. one pot is supposed to control the speed of the motor & the other pot is supposed to control the rate at which the led blinks. The switch, if on, stops control of the led & enables the ired detector to take control. When the serial monitor is open everything works like it is supposed to if I close the serial monitor the motor still spins but there is no led action & the switch (apparently) no longer controls anything either. Yes, there are differences from this board & my other uno but I'm not experienced enough to know what matters but nothing looks weird just subtly different in a few spots. Yes I will try to provide some photos but can't immediately.