This may be the wrong place to post this, if so, forgive me mods 
I have obtained a copy of the AnyConnect Secure Mobility Client from ‘various sources’ (university) and I am able to use it to connect to our resources (remote file storage)
My question is, can AnyConnect be used as a normal VPN client?
I have a subscription to PIA, and if I try to use anyconnect to connect to one of their servers, I get an error saying ‘could not connect to server’, but I’ve heard of people getting it to work
Or is it that anyconnect only works with Cisco hardware?
AnyConnect is a propriety SSL VPN client for connecting to Cisco devices only. Maybe try your luck with openconnect though.
I don’t think PIA provide this kind of VPN. You can do L2TP/IPSEC using Windows client
AnyConnect is only for the Cisco ASAs that have it enabled.
and ASR, ISR, CSR, maybe a few others.
and I believe that, although it is usually deployed with sslvpn (https) as the transport either client or clientless, it can support an ipsec mode - but i believe to ASAs only.
While not specifically relevant to your question, recent ASA code now supports standards-based IKEv2 RA vpn - so you have a variety of clients to use.
For free third party VPN clients that supports standards based IPSEC, I’ve had good luck with NCP (not free), and generally OK results with the free shrewsoft product, which works on windows 10 at least for now, but does not appear to be receiving ongoing development
