I was discharged from the military on Other then Honerable Conditions about 8 months ago.. does this affect me from ever getting a job as a local Police officer or any other government job? Is it a waste of time for me to even try ? Also should I put military on my Resume even with the Discharge I received ?

Jobs such as Police, Corrections, etc. will find out you were in the military even if you do not put it on your application. They run an extensive background check on you, so your best bet is to be completely honest.

I got an Other than Honorable with Honorable Conditions back in 2003 and since then I have applied for county and federal jobs and the discharge has never posed any issues for me. But, it does depend on what you were discharged for as to what your conditions are too.

I think they will find the military information so leaving it off the resume will cause you a problem at some point in time.
The actual reason (code) for the Other than Honorable may or may not affect the decision to hire you or not hire you. The police have to decide whether the reason would affect your performance.
But leaving it off could lead to fraud charges if you were hired and they found the info later on. Maybe you could get the opinion of a lawyer.