your iphone’s battery drained completely. there are a couple ways to get past this, but they aren’t always guaranteed to work.
attach the iphone to your computer using a separate cord. this will rule out it just being the charger itself that’s defective
try holding down the sleep/wake button for ten seconds, followed by holding down the home button for thirty seconds after releasing the sleep/wake button, this usually forces the iphone to wake up
time for a reset!
press and hold the sleep/wake button + Home button for thirty seconds at the same time. this should run a factory reset on your phone. Yeah, it’s a pain in the *** trying to get all of your old settings back, but it’s better than paying for a new phone AND getting your old settings back.
Still no dice?
try to replace the battery on your own. you’ll need a paperclip (remove the sim tray) a case opener tool (guitar picks work fine) and a #00 phillips screwdriver. flatheads occasionally work too. you can find further instructions easily if you look up Iphone takeapart or iphone battery replacement. doing this WILL void your warranty though. If you stil have a warranty and none of the above steps fixed it, definitely take it into apple.
if all else fails…
sell your iphone on ebay. depending on the model and the memory, you should be able to fetch a hundred bucks or so at least for it