Hi Booleano,
Your problems are many if you want to implement an HDMI transmitter inside and FPGA. It is extremely complicated and you need an external PHY (serializer) to convert the data to the 2.4GHz serial data that the HDMI supports.
I have done this in an FPGA but it was only supporting the low-end of the HDMI standard. You can look into the Xilinx Spartan 3A that has an internal HDMI driver IO which supports up to 720p.