You bought a wonderful car that comes with a great group of friends and virtually NO dealer support. If you want to have a bad day, take it to a Chrysler dealer and see what happens.
But if you come here, we can usually help you.
The lock thing is odd. Yes, the locks are pneumatic. The pump is in the passenger side rear wheel well. I'm finding it odd that both the fob and button did not work. Gotta think about that for a bit but a 'bad pump' would be a new one. The ONLY thing that comes to mind is a water leak that is getting the pump wet - which is a bad thing, as the pump is $250 used and I do'nt even KNOW how much new. (All pumps appear to be the same, SRT/Limited/Coupe/Roadster as far as I know - just that one or two outputs are not used in coupes.)
But that is mostly on the SRTs as their wing mount seals are suspect. The Limiteds do not, to the best of my knowledge, do that. You might lift up the mat in the trunk area and see if any of the pockets under there have water in them.
I suspect the valve gaskets were not needed at all, mine was leaking and I am in the process of fixing it - just gotta put the covers back on but it's too cold here to go out to the storage unit and work on the car (it's below 40F here in North Georgia). What leaks is the seal between the breather covers and the valve covers. (Maybe that's what they meant, now that I think about it.) I am going to change the gaskets on "general principles" but the RTV between the valve covers and breathers is what leaks most of the time.
The lock thing is kinda odd. One thing to look at: Battery. Is the battery old? If it is a white VARTA battery, it is original - change it TODAY. Look at the battery terminals and the ground cable lug where it attached to the chassis - it tends to corrode and since it is out of sight, many never notice it till the car won't run. CLEAN power provided by good battery connections, a good battery and good alternator is VERY VERY important. If you go get the battery "tested" you are wasting your time - go by the age of the battery and the symptoms.
Welcome to the group and let us know what you find under the mat or in the wheel well. I can not tell you how to access the pump, I have owned three Roadsters but not a coupe, I don't know how to get in there.
Consider coming to one of our regional or local meets - best, fastest way to learn about the car AND to meet some great people.
I offer some links to get you there:
https://www.crossfireforum.org/forum...-4-2016-a.html
https://www.crossfireforum.org/forum...ave-dates.html
https://www.crossfireforum.org/forum...14-2016-a.html
https://www.crossfireforum.org/forum...17-2016-a.html
https://www.crossfireforum.org/forum...-michigan.html (Where is the thread for THIS year's meet? GARY? )
Then there is Woodward, but I can't find that one, either....