I know this is kind of dumb but did you make sure the battery was all they way clicked in? I had a scare once because the battery was half engaged and my ronin was powering on but freaking out
c100 files are tiny compared to the gh5 and the a7s. This will vary due to the compression but I have here a five minute video out of the c100 that is just a hair under a gigabyte
I would absolutely go for it! From my experience with creating a film club in a high school, and just working with people in general, there will be people that are super invested in film and understand what it takes to create a finished work, and there are people that just wanna make movies and aren't particularly interested in the process. These people are a pain in the ass, so what I would recommend establishing to the group that there is a good deal of involvement and required to remain a member of the club. Dedicated filmmakers will understand this but it will give you the opportunity to weed out the people that will slow you down (you don't have to be brutal, they'll be running for the door pretty quickly if you make it clear how much work it takes). As long as you don't get lack of technical skill mixed up with lack of interest, you will be able to narrow down your club to other talented filmmakers, and dedicated people that are ready and willing to learn.
WARNING SE7EN SPOILER!!!!!!!!!
I am personally an advocate for the c100. The LCD is not perfect, but I haven't had any real problems with it in the past, especially with the stellar vision assist. For me, the c100 is absolutely perfect, however, for steadicam use it can be a bit of a pain. I put it on my steadicam solo, which is one of the lighter steadicams, with a very small and light lens, I even took the top handle off, and boy was it brutal on the arms. If you want to use this for any amount of time with a steadicam I suggest you hit the gym. Yes the codec is not perfect, but if that bothers you, you can get a ninja blade, this being said I have had some trouble mounting my ninja blade and keeping the camera balanced in my hands. The advantage to the avchd is that the files are delightfully small, you practically never need to worry about battery or storage space, which I find to be incredibly creatively freeing. This being said, if you are willing to put the time in money to building an a7sii setup that truly works for you, then all the power to you, its a great camera, I just want to put it out there that from a usability perspective, c100 is king, and will never fail on you, whereas the a7sii may very well overheat, run out of battery or storage space. If you are shooting and directing, I would heavily suggest the c100. If you have a dedicated person or two to run camera most of the time, a kitted out a7sii may just be the option for you, because it delivers a better image (on paper). Personally I prefer the look of the c100, but thats a matter of preference.
Not 4k but the c100 mk1 is a superb option, not to be overlooked because of its age.