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You can see the IMEI-number if you take out the label tray which is located behind the SIM-card cover. Check the following link:
http://userguide.sonymobile.com/referrer.php?region=gb&product=xperia-z1#IMEI-number.html
It's not located at the SIM tray, you should be able to pull out a label tray where you can find the IMEI-number. Are you sure that you have the Xperia Z1?
If you cannot find it,get a USB OTG cable and connect a mouse,you should be able to unlock.