ZID Controller described a near loss of separation event after noting a potential conflict but then allowing other distractions to delay required corrective action.

Narrative

A B717 was eastbound in the southern half of the APE Sector. A CRJ7 was climbing off CLE; over APE VOR going to ATL. When I climbed the CRJ7 to FL340; I saw the B717 as possible traffic; but figured the CRJ7 would top the B717 and I had plenty of time to watch and see; about 9 minutes. I got busy with aircraft climbing and descending in other parts of the sector; and had to make extra calls for coordination on other aircraft; slightly distracted. When I scanned back to that area of my airspace; I had another issue to take care of first. Then Conflict Alert advised that the CRJ7 was not separated from the B717. I was too late to vector the two aircraft; due to strong winds. I ended up asking the CRJ7 for best rate of climb through FL300; and had to beg for separation. Although separation was not lost; it was not an ideal situation; and not my proudest moment this week. Recommendation; use positive separation at all times; because even though you may have 'time to get back to it'; it is easy to get distracted.