Does it turn on when using the battery only i.e. charger not plugged in?
Try a full power refresh and check if that resolves the problem.
Here’s the procedure:
i). Disconnect the charger from the laptop, if connected.
ii). Remove the main battery from the laptop.
iii). Dis-assemble the laptop to a point where you can remove the RTC (Real Time Clock) coin cell battery from the motherboard. Note: Remember the orientation of the battery before you remove it. Usually it is +ve on top as marked on the battery.
Here’s a link to the relevant section of the maintenance and service guide for a DV5 1000 series laptop that may help (I couldn’t find one for your exact model but this should be similar).
When the RTC battery is removed from the laptop, measure its voltage. If it is <2.5V DC replace it. Usually the battery is a CR2032 type battery (marked on battery itself) and is commonly available everywhere e.g. supermarkets. These batteries are a non rechargeable Lithium battery and have a life span of approx 5 years
iv). Press and hold the laptop Power button for a full 30 seconds and then release it.
v). Reinsert the RTC battery (remember the orientation).
vi). Re-assemble the laptop and reinsert the main battery and connect the charger and try turning on the laptop.
If it starts, once fully booted, check the charge status of the main battery. If charging allow it to fully charge and then create a Win 10 battery report to check its status. Compare the Design Capacity value against the Full Charge Capacity value to know the percentage status of the battery i.e. what percentage is the FCC value of the DC value. This is just so you know how good the main battery still is.