unfortunately the I-PAC4 is gonna cost at least $77 after shipping. that is a considerable amount above $40. you really have to bend your budget around this one. you have to realize that the CP is probably one of the more important aspects of the project and it is the encoder that makes the CP.
I am also planning on building a 4 player CP and have given this A LOT of thought. There are several possibilities.
as mentioned, this is the nicest solution available but it will cost about twice what you want to pay.
my original plan was to use 4 digital psx pads and a lpt1 interface i had made. it allows for 1 joystick and 10 buttons a piece which totals to 56 inputs, (same as I-PAC4). unfortunately, although being fairly cheap for me (~$20 or so total), when i tested it, it was too much of a load on my old cpu. i can barely run the games i want on my pII but this thing slowed it down too much. i can sell this setup if someone is interested..
my next attempt was to look at a keyboard hack. the one i got ended up blocking after 8 simultaneous inputs. i believe that a keyboard hack is still the absolute cheapest way to go. period.
now most people will say it is completely unworth your time and effort to attempt a keyboard hack now that very nice encoders are available for ~$30. these options basically are the keywiz, with 32 simultaneous inputs, the IPAC-VE, also with 32 simultaneous inputs, or the mini-pac, with 28 simultaneous inputs at the moment. obviously, none of these actually meets your requirement of 44, but there are ways to work with that. For example, if you do not require all 44 to have simlultaneous inputs, you can use the Shazaam function on the keywiz. you can also use the shift function on the IPAC-VE and the mini-pac. there is a way to wire it so that the shifted function only requires one button press, but remember that any of these buttons are pressed, all other buttons will be shifted also.
if the shift/shazam thing doesnt work for you, consider adding a keyboard hack along with an encoder. the mini-pac has an active passthrough for a PS/2 keyboard which you can hack for the necessary inputs. this is the path i have settled on at the moment..
i have recently found another possible option for 40+ inputs for <$40. if this ends up working, i will definitely post it..