MONTH needs to act on a date, or a cell containing a date. MONTH(3) and MONTH(11) will always return 1, as those numbers will be interpreted as being within January 1900. Also, if you return "0" this will be a text value - you do not need the quotes around the 0. You can change my formula to include the TIME function like this:

=IF(AND(MONTH(B2)>3,MONTH(B2)<11)),IF(G2>=TIME(20,0,0),I2,0),IF(G2>=TIME(17,0,0),I2,0))

You seem to have changed the time for the winter months to 5:00pm, so I have also done this in the above formula.

Hope this helps.

Pete