The Intel Pentium G620 is Sandy Bridge. The Intel Core i3-3220T is Ivy Bridge. You will most likely need to update the BIOS for the motherboard before it can support that CPU.
Edit: Thanks @Mark Allen for the comment. I was googling the Shuttle SH67H3 when he posted and I found this support page. For the Intel® Core™ i3-3220T Processor (3M Cache, 2.80 GHz)
you will need version SH67H000.201
of the BIOS and BOM version 2.0.