Other than the MageSafe connector LED there is no other diagnostics to prove the system is able to get power.
Are you sure the MageSafe power adapter is good? Is the battery charged (using a second system if you can)?
Sometimes it's a matter of tracing out the power feeds to see whats happening. Using a multimeter you should be able to trace out the power from your MagSafe connection to your logic board. Are you able to do that?
Often times I need to replace the MagSafe DC-In board unit as the contacts are worn or damaged. Here's the IFIXIT guide: MacBook Pro 13" Unibody Mid 2012 MagSafe DC-In Board Replacement