I made a clock out of a record, powered by a solar panel and a rechargeable battery.

What you'll need:

a record
a small solar cell and battery connections (I bought a cheap solar powered garden lamp, and I removed the solar cell and connections from it.)
a clock movement (you can purchase these from places such as Hobby Lobby)
balanced clock hands (can also be purchased from Hobby Lobby)
numbers to decorate the clock face (again, Hobby Lobby)
a plate, or pottery holder
a soldering iron and soldering wire
electrical tape
a double AA rechargeable battery
and a drill press

Step 1: Preparing Your Solar Cell

Check the connections between the solar cell and the wires. Faulty connections here will prevent the rest of the project from working. If the connections are bad, a new solar cell may be needed.
Make sure the wires connected to your solar cell will be long enough to reach the battery pack, if not you'll have to solder more wire to the end.
Also, make sure to purchase a solar panel with battery connections, or, if you take the solar panel from a garden lamp, make sure you keep the battery connections from the lamp (this may require some additional soldering).
Cover any soldered wire with electrical tape for extra insurance.

Step 2: Preparing the Clock Face

Apply the numbers to the clock face. The ones I used were just stickers. Make sure you measure out the accurate distance between each number.
Next, drill two holes in the clock face to feed the wires of the power cell through to the back. I used a drill press to drill the holes close to the 12 o'clock mark.
Then, mount the solar cell to the clock face, and feed the wires through the two holes. I used hot glue to mount the solar cell.

The clock movement I bought was slightly too big to fit in the hole in the record, so I used a file to make the hole slightly bigger.
Installing the clock movement and hands is fairly straight forward. The clock movement should come with all the necessary parts.
First, place the rubber washer over the clock movement.
Next, place the clock face (record) over the movement.
Then, place the metal washer over the clock face.
The clock hands go on next, starting with the hour hand. Make sure it has a snug fit on the shaft.
Next, place the minute hand on the shaft, and place the small bolt over it.
Finally, snap the second hand to the top of the shaft.

For a temporary connection, you can attempt to wedge the battery connections into the clock movement.
My battery connections were too large, however, and I wanted a permanent connection. So, I simply soldered the battery connections on the wires to the battery connections in the clock movement.
Make sure you do this very carefully. I accidentally melted part of the plastic on the clock movement, and almost burnt a hole in my record.
Finally, place the AA rechargeable battery in the clock movement, and make sure all needed parts have a good connection.

Place your finished solar powered record clock in a plate/ pottery holder. Make sure to purchase one the comes up far enough in the back, so your record clock will stay balanced in it.
The last step is to place your new clock in a sunny location, so the solar panel gets plenty of light, and your battery is always fully charged.