I bought this MP4 player, cheap, off ebay some time back. It didn't use an internal built in battery but a removeable cellphone-style battery. So, I removed the battery, and soldered two wires to its contacts. The standard colors, red for positive and black for negative. The solar cell will have to be attached to its back as there is no space for it on the front.
I then soldered a blocking diode to the positive side of a solar cell I had salvaged from a garden light I bought at a dollar store. To make sure it would still work I connected it to a green LED and held it up to a light bulb, and the LED lit up. I have done tests with various-sized solar cells connected to lithium batteries and this one worked the best. I have also tried solar cells taken from solar powered calculators and those that powered solar powered toys and determined that the smaller cells take wayyyyy to long to recharge the battery.