There does not seem to be any replacement batteries for sale for the
Dell DJ. I did some research and found that the Dell DJ Pocket DJ
uses a Lithium Ion battery type LP043048 with 500mAh capacity. The
size is 30.5x48.5x4mm.

I used a replacement battery pack made for Apple Slim IPOD -3G. Apple
battery number 616-0159 and E225846. Google 616-0159 and you can
find many sources for this battery. I got mine on Ebay from Enessy/
Digital Power Pro for about $10. This replacement is 053048 so is 1
mm thicker but still fits.
Also the replacement is a Lithium Ion polymer with about 850 mAh
capacity, so this is good, longer run time.

The original pack has 2 wires, red and black for positive and
negative.
The replacement pack has three wires. Red Black and White. The white
wire is for thermister in the battery assembly that we don't need.
The connectors are not compatible and the wires are too short so you
have to cut the red and black wires for the old connector and solder
them onto the new battery. Just cut and remove the white wire. Take
care not to short the battery. Use heat shrink tubing to insulate
the splices. Also use insulating tape to make sure that no part of
the metal battery is exposed and can touch to any of the Dell DJ
circuits. Take care not let the battery short or overheat it when
working with the heat shrink tubing. Lithium batteries can be
dangerous. The wires are very small, you need to know how to solder
and strip small fine wires to do this.