Charging light wont turn on

I have recently found my DSi after a few years of it sitting dormant, so I plugged it in using a cord with two ends, one I plugged into my DSi and the other I plugged into my even older DS Lite. The charging light did not turn on when I plugged the DSi in, but the charging light of my DS Lite did turn on when I plugged it in. I cant turn on my DSi, but I can turn on my DS Lite. Does anyone know what the problem is and how to fix it? Thanks.