Are you sure it is charged? An update can drain a tablet's battery, if it was a large one. I would suggest first you plug it in and make sure it is actually charged. Once you are sure it is charged, try holding down the power button for about 20 seconds and see if it boots up.
Hopefully it will boot up just fine. If it powers up, but hangs or gives you trouble booting, you will need to shut it down again, and boot in "Safe Mode" to see if there is anything on the tablet that is making it not load.
If it doesn't charge, you will need to check to see if the problem is the cord, the charger port, or the battery. If it is the cord, that is easily replaced. Just make sure you get the right one, as Lenovo ones look like others on the outside, but the prongs on the inside can be different. So be sure you take the old one with you if you go to get a new one.
If the cord is fine (you can also test yours on another device to see if it is working), then you will need to check the port and the battery.
If it is the port that is damaged, that will probably require that the motherboard be replaced (they are attached). If it is the battery, you will have to open up the tablet to replace it, which is a tad more complicated than on a cellphone.
Start with the charging and see if that works.
Also, please note, if your device is under any kind of warranty, you will want to contact your carrier or the manufacturer about the issue prior to opening up the device.