ZID Controller described an apparent failed hand off from an adjacent facility that resulted in an aircraft unknowingly entering his/her airspace for some distance before positive identification was clarified.

Narrative

I was working RADAR at BOB (79). There were weather deviations and multiple restrictions from Washington Center for IAD and DCA flights. It started to get busy and I immeadiatley called for a tracker. I was also holding a DCA arrival over the HVQ VORTAC at FL350. At one point during the session; my headset and my trackers headset were not working. My D-Side had to take over the frequency for about 1 minute; until we got our problem fixed with our headsets. The D-Side working at the time was a CPC of long duration. After we got through the busy push and things were settled down; I took the position and relieved the tracker of his duties. I had a IAD arrival that needed to cross our boundary to Washington Center at or below FL290. I descend the aircraft from FL350 to FL320. At BOB (79); the altitudes are FL320 to FL350. Within 5 seconds my D-Side asked me who this intruder aircraft was at FL320. The intruder was with the aircraft with a descent to FL320; 12 o'clock and 8 to 10 miles. I immediately keyed up at stopped the aircraft descending to amend altitude and maintain FL330. This intruder aircraft was about 40 miles in my airspace and was not handed off to me; or coordinated from Washington Center. The intruder aircraft was not observed until about 40 miles in our airspace. The Intruder did have a target under him at FL290; or maybe the aircraft was climbing and that is why we thought the intruder was not seen until that point. My D-Side immediately called Washington Center and asked about the aircraft. They told us who he was and that we received track control on the aircraft and communication. Washington Center claims they tried to call us twice on the land line to tell us about the aircraft; however I do not remember nor does my D-Side remember Washington Center ever calling. Even when my D-Side called to ask who the aircraft was; I do not believe they told us they tried to contact us about the aircraft. Even if they couldn't get a hold of us why wouldn't they spin the aircraft to keep him out of our airspace? Separation was never lost in this situation due to the great scan and communication between the D-Side and myself. Recommendation; after working a busy session; just remember to pay attention a little more to all the little details like hearing the land line and listening for read back errors.