Ok - first things first. I'm assuming that you have at least a "working" computer, right? (or do you use the library, or other means)
If yes - then maybe we can use part of the 'puter as the start of the sound system and such. Answer me these q's and we'll take the next step.

Can we expect that your home pc can do these jobs? (to SOME extent?)
-At least 64 notes of polyphony - YES
-Lots of voices, including drums and drum rhythm - YES
-We need a 16 track sequencer - YES
-Floppy Disk Drive - YES
-MIDI connections to a Computer or MIDI program on a computer - YES
-keyboard to be expandable - YES


If we can utilize your pc for these tasks, maybe we can incorporate a controller of some sort to get you started, while you sock away your pennies for a better system, later.
To encompass these next features - I'm sure SOMETHING can do the job in a 100-200 price range.
-No less than 61 keys
-Controllers, like pitch bend wheel, modulation wheel
-Good sound quality!!!
**(even though the pc will be used as well)
-Would like the convenience of a LCD Display

I have a few ideas already about some options for you, but need to know if the computer is available for your music as well as general family use. I admire your strength in sharing your family's difficult times with us. It's never easy to air our dirty laundry, but we're all here to help you. I'm pretty good at horse trading, and I have lots of things I don't use anymore, so I'm trying to make a package for you to get started with. I don't want you to get the wrong idea - this is not a pity case ... I just want to help, if I can. Charity can also begin on the net!