What kind of military power did Corinth have?

Its power varied over the three millenia of its existence.

During the classical Greek period, it was a second rate power, with a navy easily beatable by Athens, and an army which was easily beatable by Sparta or Athens.

During the absence of the main army of Athens on an expedition, Corinth took the opportunity to invade. All that was left in Athens were the old men and boys not elegible to go with its expeditionary force, and these turned out and repelled the Corinthian main army. On return home, this defeated army was chiacked by the boys and oldies of Corinth and was so humiliated it went back to try again the following day. It was ambushed, with great slaughter.

Howevr it did fight successfully in cooperation with other Peloponnesian allies in other conflicts.