Welcome to the group.

Yes it is still possible to mine (see the chainz block explorer on https://chainz.cryptoid.info/gap/).

From your description of the client's behaviour it sounds like it's not finding any currently-connected nodes on the network, i.e. it's failing to sync. This can happen with elderly binaries in which the original hard-coded initial connection nodes (called "syncnodes") have long since gone away. In order to enable your client to sync to the network, you need to add the following list of node IP addresses to the Gapcoin config file, any of which should enable the client to start syncing:


Alternatively, if you are uncertain about how to change the config file, you can use the "Debug Window" menu selection to bring up a dialog box, select the "Console" tab to get a console in which to  enter the command: addnode 37.139.15.251 add followed by addnode 37.139.15.251 onetry. If your client doesn't report that it is connecting to the network, try another IP address from the list (if necessary, repeat until successful. If ultimately unsuccessful, report back here).

All the above nodes are Gapcoin nodes configured to accept incoming sync connections (the chainz list of connections includes nodes which aren't serving/listening and while those nodes do support the network, new clients can only sync from nodes configured with listen=1, described in the command-line help as "Accept connections from outside"). The reason there are so few clients that accept incoming connections is that for most home setups behind a router, enabling connections from the outside will only actually work if the router connects the client internally via UPNP).

Finally, if you prefer not to wait the several hours that it will take the client to sync, you can download a zipped current snapshot of the indexed Gapcoin blockchain which I have made available, to be unzipped in the Gapcoin data directory. When starting the client, it should then take just a few moments to sync up completely.


Cheers,
Graham