If you flash a stock rom for your carrier, you will get a modem that's presumed they tested thorougly enough so it works for most people most of the time with their network before they released the rom.
If you've got that lockscreen issue, that's a different problem, but try flashing a stock rom for your carrier (and do a wipe after) before you do anything else.
An IMEI search won't give you the info you're after. And as I said in my PP, it's not important, but to make sure of things you flash a rom for your carrier.
If it's important enough to cause you grief if it's lost, back it up. No excuses
Trolling for thanks is lame
Does Samsung's auto-brightness implementation crap drive you to self-harm ? A solution !
Most retarded thread on XDA in 2013