There is an old network saying that goes something like this......
Make just one change on a network.......and everything else on the network will change.
You will need to reset the AirPort Express back to factory default settings and then set it up again, so that it can recognize the new modem and be programmed with the correct settings for the new modem.
To reset the AirPort Express,.....assuming that it is already powered up......hold in the reset button on the back of the AirPort Express for 7-8 seconds and release. Allow a full minute for the AirPort Express to restart to a slow, blinking amber light status. That is your signal that the Express has been reset and can now be reconfigured again, just like you did the first time that you installed the Express.
If you need more help, we'll need to get the make and model number of the modem to be able to provide detailed, step by step instructions.