Why is my fridge causing my lights to dim?
I agree with Aviator, the electrician is the safest bet. From your description though, it sounds like the Compressor motor on the fridge is either seizing up or has a short in the motor winding. Why it is not tripping breakers or blowing fuses is a concern worth looking into. A qualified electrician will be able to put an amp meter on the Fridge and measure how much current draw there is and determine if it is pulling too much. 
Only two general possibilities really exist. either the Fridge is pulling too much, or your panel is not providing enough. or the two combined (okay, 3 possibilities)...