Honestly, why won't cheap things last longer than five minutes?
Step 1: Take apart the light fitting.
After you have opened it, just take off any big removable parts, taking note on how they assemble so you can fit them back on. Also remove the batteries if they are rechargable. If they are physically attached / soldered in, just leave them as they are.
Step 2: Recharge the batteries
Place the rechargable batteries into a recharger for a while. If your light hasn't been working for a while, then the solar panel will take a looong time to revive the dead batteries. This will just give the batteries a kick-start so that the solar panel will just top it up during the day.
Step 3: Cleaning time!
Next, check the circuit for damage. You should be able to work out something thats stopping the circuit from working. A good indication is rust or broken wires. Where possible, just try to replace the parts. If you haven't got spare wires or a soldering iron, just use wire cutters to strip wires and twist the ends back together. If the switch is broken, you can cut it out and twist the wires together. If the LED isn't very bright, you could consider taking it out and replacing it with a new similar LED of your choice if you know how to.