Don't know what make/model refrigerator you have *amy* - but the pan in the bottom of the fridge is generally/usually a "drip pan" which collects condensation that drips off the condenser coils (so it doesn't leak onto your floor). It also collects dust and dirt. And, when you add moisture and dirt in layers, over 10 years, it could be an ugly crumbly mess.
Since your fridge works fine, and you don't really want to replace it ... I would check to see if maybe it does have a filter that should be replaced and not chunk out a good box!
As for the free fridge - you might want to read the link I posted to the info about it in the FREE Refrigerator thread