Ok so… this a mess.
I have a spark core, connecting to a Mac, on a university network which has the spark core’s port blocked (and will never be unblocked). I also have a 3 mobile modem (with no sim card). Apparently I can use these to connect the spark core and set it up, but I have no idea how - it was done before, but the instructions I was given don’t work at all.
You're going to have to create a network to which your Core can connect. This shouldn't have those blocked ports, or captive portals. I can't tell you how to do that, since there isn't much information to go by other than
Either you figure out how to create such a network, or provide us with more information so we can help accordingly.
Then it should be just a matter of connection to that network using either the app or alternatively the CLI or even a Serial connection. If you want to, you could even go as far as flashing code over DFU-UTIL with the credentials in code, but that's a bit over-the-top.
Also, the fastest way if you use the hotspot that your mobile phone might be able to create. 
Yes… i should do that :L how do you setup a wifi hotspot that the spark core app will connect to? the app keeps asking for the phone to connect to a wifi network
You won’t be able to use the app on the phone you’re setting up the network with. You could configure the credentials using the CLI with particle setup wifi
I’m trying to do that, I keep getting back “Something went wrong, serial prompt timed out” - any ideas? This isn’t covered in the trouble shooting :-/