There is a CMOS counter chip called a CD4060 that will do this with minimal parts and no programming. However, it will not have great accuracy. The problem is that electronic circuits can time seconds, milliseconds, and microseconds with outstanding accuracy. But for longer time periods (24 hours is 86,400 seconds), "normal" timer circuits have accuracy issues. That is why longer times usually are handled by an accurate oscillator followed by a counter that just counts up time ticks until the desired time period is reached. This can be done in a small microcontroller for about $1 if you have a few months experience in writing software for it.
Another way to do this is to get a small lamp timer for around $5, plug a cell phone charger into it, and have that power the LED.
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