Is it possible to prove the identity by ip address of someone that has compromised a router on your network?
closed as unclear what you're asking by Jens Erat, Graham Hill, TildalWave, Xander, Polynomial Nov 28 '14 at 14:43
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Prove ? No. Trace back, possibly. Most likely, a determined adversary who is focused on you may have compromised one or more intermediate systems through which they pivoted their attack to obfuscate their movement. You will likely need to go before a bench to subpoena DHCP / PPPOE logs, server logs from intermediate systems, etc.
Call in a pro forensics team like Mandiant or Verizon, and coordinate with LE. Based on the questions you are asking, this is probably above your grade.