Hi @jarateman ,
Maybe first try just only charging the tablet to check if it will respond to the charger and also that the battery will take and hold a charge.
If it doesn’t hold a charge then “Having it sit on my shelf for years on end,…..” would most likely mean that the battery has become depleted beyond recovery and would need to be replaced. Use the information on the original battery to search online for a replacement LiPO battery i.e. voltage (usually 3.7V), current in mAH and dimensions of battery. (usually a 6 digit number)
After that if you have only lost the Power button actuator, (component that actually operates the switch) once you have replaced the battery (if necessary) you may be able to start the tablet by pressing the power switch inside the tablet. The switch is what the actuator would push to operate it.
Here’s the ifixit Disassembling Monster M7 Tablet Entire tablet guide that may help.
If you get it working you may have to search online how to update the Android OS version installed in the tablet as being an older tablet no doubt it is out of date and will not work with newer apps but it may depend on what you want to use it for.