Batteries are all removable on laptops, just some on the more recent ones are a royal pain to access. Personally I find it a trick to just get you to spend more either sending it in, or paying to get it fixed or paying to get it replaced (whole device).
If the device is blinking no matter if the cord is attached or not, it is the battery. It is quite common for that to happen. So if your device is under warranty, I would contact the manufacturer about getting it replaced.
It does turn on, the power adapter has worked on other laptops, and i havent ever replaced the battery (it dosent even have a removable battery, you have to open the case). which is why i dont want to remove the battery although i think i might replace the battery if i end up inside the laptop and try the 30 second power button method
It could be a few things. The adapter, the battery, both. If you aren't using the original battery it could be the new one isn't correct (happens a lot) or if the charger isn't original it can be not putting out the right power (also happens a lot).
Try the following and see if it will turn on.
1. First make sure the battery has a charge.
2. Unplug your charger cord.
3. Remove the battery.
4. Press and hold the "Power" button for 30 seconds and see if the device will turn on.
5. If it does, great, if not yet, no big deal. Now plug back in the power/charger cord. (If it didn't turn on without the cord in, it should turn on once you it is in. Yes sometimes they will turn on, or try to turn on, even with nothing attached/plugged in.)
6. Now put the battery back in.
If this doesn't help, then test the power cord to see if it is good. Either try your cord in another device, or try another devices cord in your laptop.
Should that not be the problem, then check the battery to see if it needs replacing.