Can supplying DC power into an AC device break the device?
It could be broken. Supplying ac to an electromagnet can produce an ac current of maybe a few hundred milli-amps. Supplying the same coil with DC could cause the coil to take a high current of several amps. This could easily burn-out the coil after a few minutes.

But, it could be the DC power source that broke - you need to test it with a voltmeter. If you don't have one then you need to find someone who can do this for you.

Once you have a voltmeter, check to see if it can measure resistance and connect it to the AC device to see if you can measure resistance between the two terminals. If it measures a few ohms then the ac device is probably ok - this should be confirmed byt the output of dc power source being open circuit or low voltage.