Help! I think I've been blacklisted. . .

I was terminated from a past employer under dubious circumstances. To make a long story as short as possible, it was necessary for me to utilize a sick day to visit a hospital -- I was having severe chest pains and my wife believed it may have possibly been the beginnings of a heart attack. At the hospital I was told it was a highly acute case of nerves and was told to take the next few days off from work, and was given the appropriate documentation to substantiate what the doctor's recommendations were. Contrary to the doctor's advice I went into work the following day (as I prefer to believe that I have a good work ethic and did not care to see even more work pile upon my desk), but was forced to leave at 12:00 (noon) due to a recurrence of my chest pains. The company used to different mediums to verify login/logout times -- our phone system and our computer system. According to the phone system I logged in at 8:55 A.M. and logged out at 2:30 P.M., whereas according to the computer system I logged in at 9:15 A.M. and logged out at 10:55 A.M. What had happened is that I came in at 8:45 A.M., not feeling very well and needed to visit the facilities. After a few hours my chest began to ache with renewed intensity and I was forced to leave. I logged off from my computer at the notated time (10:55 A.M.) but was caught by several incoming phone calls before I could abscond -- which kept me at work for yet another hour. I forgot to log off from my phone (which was later done by someone else -- whom I am not certain, but I was logged off). Two or three days later I was called into the Human Resources Interview Room and informed that I was being terminated due to Timesheet Falsification. I had written on my time sheet that I was in the building and ready to work at 9:00 A.M. and had left at 12:00 P.M. The individuals who informed me of my termination only presented me with my computer login and logout times, but refused to even acknowledge my phone records -- records which clearly placed me in the building at 9:00 A.M. and showed me receiving three inbound calls -- the last of which was ended at 11:58 A.M. At the time of my "Exit Interview" I was given documentation (signed by both myself and a representative of the HR Department) that my (now former) employer would only verify the dates that I was employed, my position title, and my salary, and would not make any other statements whether good or bad about my work performance (which had been praised by my supervisors and co-workers, and should normally have been a shining beacon on my resume). With this said, I have been searching for a new position for the last 9 months and have had absolutely NO success (I have submitted my resume and applications to over 300 various employers and have acquired nothing). My only conclusion can be that my former employer has been giving me a highly detrimental reference. I have not been applying to positions for which I am either over or under-qualified, nor have I ever committed a crime. My disqualification from the myriad of positions that I have applied for can only lead me to believe that I have been "blacklisted" by my former employer. My question, for all the length of the explanation, is simple: what recourse do I have against my former employer? The laws cannot be such that I must simply sit by as my family (wife and 2 young sons) falls into financial ruin because of the vindictiveness of a past employer. What can I do?