If your Node Manager complains during start-up that it cannot read its state:

java.io.IOException: Invalid state file format. State file contents:
at weblogic.nodemanager.common.StateInfo.load(StateInfo.java:135)
at weblogic.nodemanager.server.ServerMonitor.loadStateInfo(ServerMonitor.java:475)
at weblogic.nodemanager.server.ServerMonitor.isCleanupAfterCrashNeeded(ServerMonitor.java:139)
at weblogic.nodemanager.server.ServerManager.recoverServer(ServerManager.java:255)
at weblogic.nodemanager.server.DomainManager.initialize(DomainManager.java:103)
at weblogic.nodemanager.server.DomainManager.(DomainManager.java:55)
at weblogic.nodemanager.server.NMServer.initDomains(NMServer.java:219)
at weblogic.nodemanager.server.NMServer.start(NMServer.java:199)
at weblogic.nodemanager.server.NMServer.main(NMServer.java:355)
at weblogic.NodeManager.main(NodeManager.java:31)

then you need to remove the following file:

d:\bea\user_projects\domains\$DOMAIN_NAME\servers\C_0-S0\data\nodemanager\C_0-S0.state