Firstly you need to add the BootStarterReceiver to the manifest:
<receiver
android:name="com.nu.art.cyborg.common.utils.BootStarterReceiver">
<intent-filter>
<action android:name="android.intent.action.BOOT_COMPLETED"/>
</intent-filter>
</receiver>
Or just enable the BootStarterReceiver if you are using the latest(0.8.11 +) Cyborg version:
<receiver
android:name="com.nu.art.cyborg.common.utils.BootStarterReceiver"
android:enabled="true"/>
You'd also need to add the respective permissions:
<uses-permission android:name="android.permission.RECEIVE_BOOT_COMPLETED" />
One this setup is done, choose your boot handling module and implement the OnBootCompletedListener, in the onBootCompleted method perform your code there.
As for staring a new activity at that point... I am not sure how your users will respond to that, but you can call cyborg.startActivity(), with an intent that will launch Cyborg's default ApplicationLauncher, and add the FLAG_ACTIVITY_NEW_TASK.
public void onBootCompleted() {
Intent intent = new Intent(getApplicationContext(), ApplicationLauncher.class);
intent.setFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
cyborg.startActivity(intent);
}