Rechargeable batteries, whether NiMH or Lithium-ion have a limited number of charge/discharge cycles (typically 500-1000) before they begin to lose capacity. I believe the dropoff can be fairly rapid.
It sounds like the off-brand charger may have been the wrong voltage. Measure it with a voltmeter if you have one to compare it to what it should be.
As to the replacement battery, you can buy a new aftermarket battery on eBay fairly cheap, but it will have lower capacity, and likely a much lower number of cycles; or you can go to a place like BatteriesPlus, pay three times as much, but get a battery (e.g. Ray-o-Vac) that will be at least as good as the original, and will also last a lot longer. I'd go cheap only if battery life is not important to you.