When a DMP is not displaying any output on the connected screen, the problem can vary from a connectivity/network issue to a misconfiguration to a software problem to an hardware issue. So it is important to perform a good problem diagnosis by following some essential steps.
The first thing to check, is to see if there is any light turn on on the DMP. The green power led should be on all the time.
In case the box is not powering on at all and you don't see any light on the DMP, would be good if possible to test with a different power cord if available. If the same issue is present with a different power cord, there is likely an hardware issue internal to the DMP and the device will have to be replaced.
The red led is on when the DMP is performing acquisition of a network address. If you see the DMP red led staying on for long time and nothing appearing on the screen, it normally means that the DMP is not able to get an IP address from the DHCP. DHCP is enabled by default on the DMP. So the first thing to check at this point would be if the DMP is connected to a network segment where a DHCP service is available. If this is the case, it would be useful to get a span of the switch port connected to the DMP to see what exactly is happening at network level with the DHCP negotiation.
One additional test which can be done, to make sure there is not a misconfiguration on the device, is to restore the DMP to factory default. This can be done by keeping the RESET button on the back of the DMP pressed for at least 10 seconds. You should hear at least two "beeps" in a row while keeping the button pressed, if you hear only one it normally means that the DMP is just rebooting but not restoring to factory default. Then you can connect the DMP to a network segment where DHCP is available and check if it is able to get an IP address after that. This factory restore procedure is the same for all DMP models, but the DMP-4310 does not perform any "beep" when executing it.
Another thing to check is listening to the "beeps" when the DMP is rebooted or connected to the power. You should hear two different "beeps" at bootup, with a different tone. If only a single beep is heard (or no beep at all), this points to some errors during booting. This could be caused by an hardware failure (for example, the DMP internal memory broken causing failure at bootup). Again in this case, it is recommended to attempt restoring the DMP to factory default as explained above, if the problem is persisting the device will likely need a replacement. Again as mentioned before, the DMP-4310 does not perform any "beep" at all and this is expected behavior.
Finally it is always important to know if the problem is present since the initial boot of the DMP, or the DMP was working fine for some time. If it was working fine before, knowing the last known activity performed on the DMP would be useful for additional problem isolation or problem reproduction attempts.