How long does it take for a case to be dismissed or dropped if they cannot find the one who originally filed the charges?

The prosecution of a charge is governed by the statutes of the state in which the charges are filed.  Generally there are procedural codes that govern both Criminal and Civil Prosecutions.  In a criminal proceeding the prosecutor is required to present their case within a certain time frame or the matter is dismissed usually by the Judge right from the bench.  Defendants are given much more leeway time wise to proceed and granted adjournments more liberally by the Court.  Seek advice from a criminal attorney in your area.  He or she should be able to tell you failry quickly when the matter should be done with.  Good luck.