Sadly, you told us nothing about this hardware, other than its a laptop.
A battery should last much longer than two years - unless badly abused. Such abuse is typically related to heat - leaving the laptop in a hot car, for example. Or very rough handling.
There is a misconception that leaving a laptop battery plugged in will damage the battery - at least on newer laptops. This started long ago when NiCad batteries were commonly used. They suffered from "memory effect". While today's Li-Ion batteries can too, it is to a much lessor effect and typically can be reversed simply by letting the battery run down every so often.
My Toshiba laptop was plugged in almost continuously 24/7/365 the last 11 years of its 12 year life - using the original battery the whole time. When new it supported the laptop for nearly 2.5 hours. After 12 years, just under 90 minutes - but that loss is pretty typical for any battery. The only "maintenance" I did for the battery was once every couple months, I unplugged the charger and ran the laptop until the battery's monitoring circuits told me it was shutting down in two minutes. Then I plugged it back in and was good to go.
The reason why it is not a problem is because laptop charging circuits are not stupid. When the battery is charged, they stop charging the battery.
Now of course, there are exceptions. There could be a fault in the charging circuit, or battery.
Some laptops will run just fine while plugged in with the battery removed. Check your manual. If yours supports that, try that. If yours runs, the charger is fine.
As for that cable, I do not see any exposed wires but that does not mean there could not be some hidden. Or there could be some pinched wires, or broken connections.
IMO, you need to take that to a qualified technician for troubleshooting, evaluation, and [hopefully] repair. If your current battery has failed, that bad cable could be the reason why and putting in a new battery without fixing that cable could just destroy the new battery too.
A battery should last much longer than two years - unless badly abused. Such abuse is typically related to heat - leaving the laptop in a hot car, for example. Or very rough handling.
There is a misconception that leaving a laptop battery plugged in will damage the battery - at least on newer laptops. This started long ago when NiCad batteries were commonly used. They suffered from "memory effect". While today's Li-Ion batteries can too, it is to a much lessor effect and typically can be reversed simply by letting the battery run down every so often.
My Toshiba laptop was plugged in almost continuously 24/7/365 the last 11 years of its 12 year life - using the original battery the whole time. When new it supported the laptop for nearly 2.5 hours. After 12 years, just under 90 minutes - but that loss is pretty typical for any battery. The only "maintenance" I did for the battery was once every couple months, I unplugged the charger and ran the laptop until the battery's monitoring circuits told me it was shutting down in two minutes. Then I plugged it back in and was good to go.
The reason why it is not a problem is because laptop charging circuits are not stupid. When the battery is charged, they stop charging the battery.
Now of course, there are exceptions. There could be a fault in the charging circuit, or battery.
Some laptops will run just fine while plugged in with the battery removed. Check your manual. If yours supports that, try that. If yours runs, the charger is fine.
As for that cable, I do not see any exposed wires but that does not mean there could not be some hidden. Or there could be some pinched wires, or broken connections.
IMO, you need to take that to a qualified technician for troubleshooting, evaluation, and [hopefully] repair. If your current battery has failed, that bad cable could be the reason why and putting in a new battery without fixing that cable could just destroy the new battery too.
