Batteries won't charge
There are a few reasons why a battery won't charge. Make sure that the contacts on the phone and the charging cradle are clean. (Unplug the base or charger.) A pencil eraser is good initial cleaner; electronic contact cleaner sprays are a second option. Remove the battery and check the contacts inside the handset and the battery as well. Next replace the battery pack. If you add a comment with your phone's model number, then I can try to find the correct battery. (Stores like Battery Mart may have a compatible battery.)
The final possible problem is that the charging system is bad. If your phone has multiple handsets, try a different charger. If the phone allows you to add handsets, try getting a new handset. The new handset will come with a new charger. (I've never seen the chargers sold without the handset but you could try Uniden customer service. If the base station is the only handset cradle, you'll probably need to replace the phone if a new battery and clean contacts don't work.
If your Uniden phone is under warranty, contact the company.
I hope this helps.