Hi @Markie T.
The BIOS may have become corrupted, preventing the laptop from turning on.
Try a power refresh to see if this resolves the problem.
Here’s the [https://download.lenovo.com/ibmdl/pub/pc/pccbbs/mobiles_pdf/t420s_t420si_hmm_en_0a60241_07.pdf|hardware maintenance manual] for the laptop which will help you to do this.
Disconnect the adapter from the laptop, if plugged in.
Remove the main battery from the laptop.
Disconnect the backup battery. Disconnect the battery by the plug and not by pulling on the wires. (see p.83 in the manual)
Press and hold the laptop Power On button for 30 seconds, then release.
Reconnect the backup battery
Reinsert the main battery, reconnect the adapter and try to turn on the laptop.
If it starts there may be a message about resetting the date and time. This is normal.
'''Note''': While you have the backup battery (aka CMOS battery) out, check its’ voltage. If it is <2.6V DC replace it. This battery is a non rechargeable battery and has a life span of about 5 years. Its’ purpose is to maintain the BIOS settings when the laptop is switched off. When its’ voltage gets below a certain point this becomes harder and may result in corrupted BIOS settings which can cause the laptop not to start. Search online for ''04W3253'' to find suppliers