I share your concern about having to give up on an old piano.
If you're thinking of reselling it, it's very probably not. These are available for free all over the country. A rebuild sufficient to make it playable is probably more than double what it would be worth afterwards (probably no more than $2000). Here's an example of the fatal problems inside old pianos that are hard to see: http://www.chicagopianos.com/wanted.htm
"Pianos" and "basement" are two words you never want to hear together, because basements are usually damp. If they're dry, it's often because of baseboard heaters, which also damage pianos. ("Mold" is another word you don't want to hear!).
Other factors may go into your decision, such as if it has sentimental value. Some of them can sound fairly nice, as the large size allows a good scale. Many have ornate cabinets with wonderful veneer; it doesn't sound like this is the case here.
Sometimes replacement parts are just not available. There were many different designs in those days.
They can make great desks: http://pianodesk.com
If there's ivory on the keys, it can be salvaged. The back posts are probably very good wood, too. Just be careful moving it: it's very heavy, and it's tall, and it's *top-heavy*. Typically there's a person on each end of the piano, but it falls over on its keys (or back).
Ask your local technician for an appraisal. You can find one on this board or at www.ptg.org.