If all the other methods do not work it could be the obvious and often is. The batteries on these units are known to be faulty and not just because of use but they have a PCB inside them like most batteries do these days. Something in that part is what I suspect stops the battery from accepting a charge. Usually if all else fails a replacement battery will do the trick. You can find them here for a decent price. I got a few myself using "best offer" and they accepted at a very reasonable price. Here is the link: http://www.ebay.com/itm/Google-ASUS-Nexus-7-Nakasi-3-7V-4270mAh-16Wh-Li-Polymer-C11-ME370T-Battery-OEM-/161531962605?ssPageName=STRK:MESE:IT
And in case you have a 3G/4G mobile version (ME370TG) you will need a different battery here is the link to those: http://www.ebay.com/itm/Genuine-Original-C11-ME370TG-Battery-4270mAh-for-Asus-Google-Nexus-7-Tablet-NEW-/400767122124?ssPageName=STRK:MESE:IT
Good luck
P.S. Don't assume always that because you don't see anything it isn't powered on. It could be but nothing on the display which could mean the LCD flex cable is loose or needs to be replaced. IF it needs to be replaced you should be able to find them from the same seller on eBay. FoxPCParts They have a good selection of Nexus and other tablet part replacements. Maybe not the cheapest I've seen but fast shipping and everything I've purchased has included cameras etc and was packaged well and even the bootloader was unlocked which was a bonus to me.