The answer you got is correct for your initial conditions -- you specified 0 for c[0] and no velocity (c'[0]) so the system cannot move.

Try changing the initial condition and you get a different response:

DSolve[{0==c''[t]+100/0.001 c'[t]+c[t]/(0.001*0.0005),c[0]==0,c'[0]==1},c[t],t]//Simplify

to get

(* {{c[t] -> -0.000010004 E^(-99980. t) + 0.000010004 E^(-20.004 t)}} *)

Welcome to Wolfram Community! Please make sure you know the rules and how to format your code properly, which you can find here: https://wolfr.am/READ-1ST If you do not format code, it may become corrupted and useless to other members. Please respect the rules.