Corky Baxter was quite different from his pre-crisis counterpart. In 1959 (our time) the Time Masters were introduced in Showcase #20. Two years before Marvels' Fantastic Four had their own foursome of a genius, his girlfriend, her kid brother and the jock best friend would take their fateful rocket trip. Corky was the little brother of Rip Hunters' love interest Bonnie Baxter. In those days he acted as the proper Silver Age sidekick: always excited about their adventures and in awe of his role model. In the Post-Crisis mini series writer Lewis Shiner had a different take to the characters of the Time Masters.
While two new members were added (Tony and Dan Hunter) the core four all had changes in store for them. Some changes were more subtle like with Rip Hunter, while others were bolder and much more noticeable. Corky for example was no longer the happy go lucky kid he had previously been. He now had a history of drug problems and a bleak outlook on life in general. Not many connected with the teen but he found a new thrill in time traveling. His role help set the tone for this new version of Time Masters.
Where is he now?: Since the series Corky Baxter has yet to make any appearances although his fate has been hinted at in the second Booster Gold series.