Welcome back, If you don't have your keys you can not access them as the only way to login to splinterlands is your posting key. The steam keychain is now not working, check if it working with you then export your keys from steem keychain.

Steem forked to Hive, you can login to HIve with your old Steem keys and Splinterlands also moved the Hive blockchain so to login to your splinterlands account you need your Hive account keys.