Ok, I have had this problem before. I have a gt-p3113 esspressowifi, your version is the gt-p3110 right? If it is the gt-p3100 w/SIM card, the ROMs for the 3113 and 3110 will not work for it, so make sure you have the right version for your tablet.
Next, disable the MD5 check in the recovery, I found out that the ROMs for the 3110 and 3113 are near identical except for the IR blaster on the gt-p3113, so both should work for the same tab. If all else fails, open the ROM on your computer as a zip file and change the build.prop to conform to your device. Also, change the updater script, but you shouldn't need to do that.
To test this theory, go to CyanogenMod and download the three ROMs for 3110, 3100, and 3113 and try all three of them after of course be sure you're rooted, latest recovery {Philz touch, CWM, TWRP, etc} and SuperSu binary.
I used ODIN 3.07 to flash the CF-autoroot file {search CFautoroot} on Google search or whatever, install the correct USB drivers for Samsung mobile devices on your computer, then reboot your tablet to download mode by turning the power off then turning it back on pressing the power button plus the volume down button at the same time {green Android comes on screen with a warning about software}. Flash the CF-autoroot targz or md5 file with ODIN 3.07 then use whatever ROM you like.
If you still have a problem, you should start over with the stock ROM from Samsung Kies, then do this process over again because maybe you are missing a step here and may need to redo the whole process to bring the root back and open the bootloader.
By the way, to open the bootloader, you should have Android Debug Bridge on your computer. The process is as follows: boot to download mode, open the ADB terminal, connect your tab to PC, then enter the command fastboot devices. It should show your device number in the terminal window, then enter fastboot oem unlock. Might be different, but you shouldn't need to do that anyway.
But if you still need to unlock it, try Odin with the CF autoroot bootloader flasher zip file to flash the new compatible bootloader. Here are the instructions I found: Hope this helps.
If you still need to fix this problem. {copy or type this into browser} = [GUIDE] Galaxy Tab 2 10.1 OR 7.0 Rooting/CWM… | Samsung Galaxy Tab 2 | XDA Forums http://forum.xda-developers.com/showthread.php?t=1722745
