Absolutely go to the dealership. I agree that with the radio not working, it might be something else that is the issue (need a new fuse, possibly)...
Yes I would definitely have the key fob tested and keep your fingers crossed and it's not another underlying issue the radio is what makes me think that you may have somewhat have another problem but I don't want to get too stressed on it so I would definitely take it to the dealership and have them check it out
I would suggest having the key fob tested at the dealership and they can check if the battery in it is dead or not
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