Dell Inspiron 14R 5420 intermittently fails to boot

This is probably a motherboard issue

Your symptoms strongly suggest an electronic problem in the motherboard, since you've noted that it always happens before Windows starts booting up. It's quite unlikely that a laptop AC adapter would do this as the battery should be able to keep the system running even if the adapter failed. If you can confirm that the battery charges, your AC adapter is most likely good. Note that the CPU and GPU are soldered onto the motherboard on this laptop.

A hard drive failure wouldn't cause these kinds of boot-up issues as the system should be able to get through POST, just not load the OS. Bad or improperly-seated memory wouldn't explain this problem, either, as this would manifest as frequent random system and application crashes or the system giving a beep code when powered on, respectively. It's incredibly unlikely that these parts would cause the system to not clear POST with nary a beep code.

The motherboard is almost never a user-serviceable part in any laptop, so you should send it back to Dell for repair. Be sure to back up your data—the best way to do this is to remove the hard drive from the computer, put it in an enclosure, and plug it into another computer for data transfer or imaging.

See the problem-diagnosing chart in this answer.

Based on that chart, the problem is either a Power Supply failure or a motherboard failure. I would favor a motherboard failure, since you say that the laptop works perfectly well when it boots up successfully, but you could further test this by using stress tests of CPU and GPU, to see if any power problem occurs. If none happen, then the problem is probably with the motherboard. See these test tools.

However, since you still have warranty, it wouldn't make any sense to fix this yourself, since simply too costly. In addition, by opening up the laptop you take the risk of voiding your warranty.

My best advice is to use the warranty and have the laptop repaired or replaced.