Hello,
Can you check the files std_server.out or similar, you should be able to find the root cause of the issue there.
Config tool should let you login even if server isn't running.
If you can't get into config tool, potentially your connection data for config tool isn't accessible.
Search on help.sap.com for location of Config Tool Configuration files, they contain location of your connection string for config tool.
Regards,
Siddhesh