Have you got this laptop up to date like and with all of its window's updates, Intel updates and NVidia updates, and have you ever updated the bios? As what you are experiencing should not be happening with a new battery swap, Do a CMOS reset (see below) and also take the rtc/bios battery out and main battery out and ram also, leave all components disconnected for 15min and reconnect all and then reboot, as all this will reset the super IO and bios. If all this does not work, then its an internal circuitry issue that when your old battery was inflated could have damaged internal components, take your laptop to an experienced technician, who will diagnose your laptop more internally as resets and taking the battery and ram out is just an initial reset.

@Shane2goated

If it is still not working..

It might also be the issue with battery, charger or power outlet.  Try to use the charger in a different room on a different power outlet. Try to bypass the surge protector and connect it directly to power outlet.  Try to use an alternative charger if possible.  Try to turn on the computer without the charger and check it ( as long as the battery is not drained out )  

I am really sorry for the inconvenience..  Let us do the basic steps first..

Doing the power drain and bios defaults will really help. Kindly follow the steps given below:

Turn off the laptop. Disconnect or unplug the charger cable, devices or any other cables connected to your laptop. Close your laptop. Turn it upside down. On the bottom of the laptop, you can find a pin hole. It is a tiny hole. You can a find a battery symbol indicator next to the hole. It is like a + and – sign symbol as though somebody is trying to shift the battery out. Insert the pin on to the hole for 30 seconds. Remove the pin. Flip the laptop. Connect the charger cable, turn on the computer. Only on laptops where the battery is inbuilt you can find the battery reset hole on the back of laptop.

If you don’t find a pin hole on the back of laptop then you might be using removable battery. There is no need to unscrew anything to remove the battery. Turn off the laptop. Disconnect or unplug the charger cable, devices and any other cables connected to your laptop. Close your laptop. Turn it upside down. On the bottom of the laptop, please look at the top or bottom depending on the way you look at it. You can find a long door. It is a battery removable door. Just below that you can find a latch. If you move the latch you can remove the battery door. Once the battery is removed, flip the laptop. Open the top cover, press and hold the power button for 1 minute. Connect the battery back on the back of computer. Connect the charger cable back and then turn on the computer. 

If you don’t see a reset pin hole on the back of laptop or if you are not able to remove the battery (if it is inbuilt) then please unplug all the cables and devices out of laptop.  Hold the power button for 1 minute. After releasing the button you should wait a while before plugging in power. Just because the button has been pressed doesn’t bleed off all the residual electricity on the motherboard. Wait 15-30 minutes before plugging in power. Then once power is connected wait for a full battery indication before turning the system on. That allows the battery to fully reset it’s internal statistics.

Connect all the cables back and restart the computer.  

While turning on the computer, tap f2. It will go to bios. Press f9 once. It will show load bios defaults with a yes or no popup. Press enter. Popup screen will disappear. Press f10 once. It will show save changes popup with yes or no. Press enter. Computer will restart and it will load into windows.  

It might also be the issue with battery, charger or power outlet.  Try to use the charger in a different room on a different power outlet. Try to bypass the surge protector and connect it directly to power outlet.  Try to use an alternative charger if possible.  Try to turn on the computer without the charger and check it ( as long as the battery is not drained out )  

Try windows x 

go to device manager 

expand Battery

right click on all the items below battery – uninstall 

Restart the computer 

It should work fine.. 

>>>I then shut it down and unplugged it after I went to sleep and now the problem is still there and it refuses to power on. The battery led still works and is blue.>>>

How could the battery LED still have worked if it was unplugged?

>>>after replacing the battery which was inflated,>>>

When you opened it up, did it seem to be distorting or putting pressure the bottom cover, top assembly, or mainboard?

Check near the RAM sockets for a spring-loaded safety interlock switch (SW2) in diagram below. This switch must be fully depressed by the bottom cover. If bottom cover is loose or misaligned with the switch, all power to the mainboard is cut off. Sometimes it helps to tape a spacer on the bottom cover so it presses harder against the switch button when assembled.

Is there a battery disconnect pinhole on the bottom cover so that you can depress & release the other spring-loaded switch (SW3) with a paperclip without having to remove the cover?

Unplug the charger. Try gently depressing the spring-loaded normally-on switch button with the paperclip into its off position.

Then while still holding gentle pressure, try to angle the paperclip so it slips off the button. Then the button should abruptly pop back up into the switch's normally-on position. Repeat a half dozen or so times to help clean the switch contacts just in case they aren't making good electrical contact in the normally-on position.