Stereo will not power up after replacing the battery

You say that you had the battery changed, did they put a jumper wire so you would not loose all your vehicle setting? you can try disconnecting the positive side of the cable going to the battery, ground it out to the negative side, this will clear any and all settings. leave it like that for a minute or two, then connect the battery wire, you might have to drive the car for about thirty miles before the computer resets. I hope that is all that it needs. You did say the radio worked all right before you switched batteries. Check all the wires going to the battery along with other positive wires to make sure they are clean and tight. I believe there is a fuse box under the hood. (not sure) If there is check all the fuses to make sure they are good. there may have been a power surge and blown out one of the fuses.

You should be using a voltmeter or at least a twelve volt test light and make sure both sides of them fuses have voltage when they are supposed to be hot.
Is this a base radio, premium, etc?
It should be fuse #8 in the fuse panel B under the hood left side.