Macbook Pro A1398 Battery Low does not boot up with cord

A1398 looks up to MacBook Pro 15-in Retina display MacBook Pro from 2012 through mid-2015. These Intel processor models do Not have a T2 chip. They feature a separate System Management [micro-]Controller (SMC) chip that manages battery and charging, fans, and Intel CPU clock generation.

Unless and until you can charge that battery off the red zone, the battery will drag down the possible voltage and preclude starting up.

you can try an SMC reset:

Reset the SMC of your Mac - Apple Support

Make sure that the five pins in the MagSafe connector are shiny and clean (both sides), and appears to be making good contact.

Remove the Power adapter body from the wall outlet and allow it to 'rest' for a minute or two, so that it can reset itself.

What you would like to see happen when the power adapter is connected is a Lightning Bolt appears, indicating that the power adapter was detected and charging has begun. In some cases a plug icon may appear, indicating the power adapter is detected.

There is no penalty for performing the SMC reset multiple times. Be certain you are using the keys in the keyboard POSITIONS indicated -- the keys with the same labels on the other side will NOT do the trick.

The green and amber LEDs in the MagSafe end are set by commands from the computer, only. Seeing them change at all says the computer has some life to it. Although that may only mean the T2 chip is alive.

The amber LED is lit when the T2 (or SMC on older models) commits to charging the battery. (in later models, Amber may stay lit when 'charging on hold', but that does not apply here.).

If yours has a T2 chip, it is likely to be a 2018 model or more recent.

If after an hour or more of amber LED ON, if no progress is made towards a charged battery, then the battery (or possibly charging circuitry) has likely failed.

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Apple battery service typically runs about US$250, and on many models will include a refurbished (like new) keyboard and a 90 day warranty as all Apple repairs include.

HOWEVER, battery service is no longer available for Macs 2015 model-year or older.