Simplest way to find the PID of your app
You should be able to run a shell command from adb:

adb shell ps | grep your.app.name


And that will return details about your process.  The second number will be the PID of your app.  This is if grep is installed.  If grep isn't installed, you can just run ps and it will dump all processes to your screen.

You can dump logcat to a file to retroactively look at processes (up to a point) 
logcat &gt; /sdcard/logcatDump.txt

However, logcat data is stored in memory so it will all be lost after a reboot.