Let me help you with this.
The processor in mentioned works at 77W but there is another version (low power consumption) model Intel® Core i5-3550S that runs with 65W.
You can check this information at the following link:
Based on the information Gigabyte provides about processor compatibility, it seems your motherboard should run this processor. Here you have the processor compatibility list from the Computer Manufacture:
In the case the system is not working fine I would recommend you checking all connections on the motherboard and if possible testing a different processor. By doing this we can discard issues either the processor or the motherboard.