Ice maker leaking?

I have a JC Penney Refrigerator, approx. 25 yrs. old, Freezer on top with icemaker. Icemaker has been running continuously for last 10 Mon. due to the medical need of the ice. I noticed water collecting under the 2 crisper bins about 3-4 mo. ago. The icemaker also slowed down about 2 mo. ago to the point no ice was coming out due to no water was going into the tray. We solved this by defrosting the line where the water entered to fill the ice tray. There was a frozen plug at this point. Since then water has been accumulating faster under the bins. Where before I would dry it out every 10- 14 days now I have to dry it out every 3 days so it doesn't overflow. I shut off the entire fridge and icemaker for approx. 8 hours. I turned the fridge back on but left the icemaker off another 8 hours. Water did start to accumulate however slowly during this last 8 hours. I failed to turn the water supply off to the icemaker. Should I try again with turning the icemaker and water supply off or do you know what my problem might be? Is it time for a new fridge?