Check balance of inactive account on EVE

Solution 1:

Nowadays, EVE Online is free to play. There is the concept of "clone states" which are defined as Alpha Clones and Omega Clones. When you are playing for free, you play as an Alpha Clone, which comes with several restrictions on the skills you can learn and train. If you subscribe or use a PLEX, you'll play as an Omega Clone, which allows you to play as you normally would with no additional restrictions in terms of skill training or use. There's plenty of other information about the various differences, which you can read about in other questions, but they're not relevant to your question here.

What IS relevant, though, is that you can now play EVE Online for free. Simply log in and start playing! If you're still concerned about your ISK balance, there are no currency restrictions, so just open your wallet and do what you would normally do with your ISK.

Solution 2:

I'm not sure if you you can get a full API without being subscribed, but if you can get access to the accounts full API (by logging into the site and going to the API section), you should be able to use that with a program like EVEMon which can tell you your balance as well as skill levels.