I applied for an expungement in 1999 and it was denied due to a new law that applied gun specifications even though the gun charge was dropped.
Yes, it's possible. A pardon by the Governor is a power given to the Governor by way of the Ohio Constitution. It is virtually without limit (except it cannot be used for federal offenses or convictions in other states.) The Governor has the power to pardon offenses, even if the offense was not expunged as the expungement power is a judical power created and limited by state statute.
However, that being said, pardons are INCREDIBLY rare. There is no threshhold standard an applicant can meet in which the Governor is legally compelled to issue a pardon. The Ohio Constitution makes it completely clear that it's a discretionary act of the Governor that has no real standard. A Governor, in fact the same Governor, can pardon one person who's situation is practically identical to yours and deny your petition. The Governor does not have to justify his reason in denying a petition for a pardon. No court can compel a Governor to issue a pardon. And most, in fact nearly all, petitions for pardons are denied.
The process begins with a petition to the Ohio Adult Parole Board. They review your petition, your case file, and may forward your petition to the sentencing court and prosecutor to file their response to your petition, and eventually the Board makes a recommendation to the Governor as to whether approve or deny your petition (you might be given a hearing in front of the Parole Board before it votes to make a recommendation, but that's not always guaranteed.) Although the Governor is not compelled to follow the Board's recommendation, Governors have traditionally not broken with the recommendations of the Parole Board.