First thing I would do on a “no boot” with fan issues is check the RAM - see if there’s an issue with how it’s seated, or potentially a bad module or two. If you have 2 modules, take 1 out at a time and see if you can get it to boot - if so, that module is bad. At that point, your best option would be to buy a matched set of RAM and replace both of the original modules to avoid any future compatibility issues, if you’ve confirmed there are no other issues. Follow this guide to access the RAM.
If the issue persists, try and boot the computer without the hard drive. Some of these consumer machines (including Dell) are temperamental about booting with a failing/failed HD installed. Refer to this guide to remove the hard drive. I’ve never had an issue with the business Dells booting with degraded drives, but they tend to make the BIOSes more resilient to bad hard drives/RAM on the business computers, and least to the point it can push an alert and then beyond that it's still anyone's guess. It’s not unheard of, so don’t ignore the possibility - especially consumer systems!
The point of the alert the user POST survivability is let's say the SSD is failing in my E6440. I have it set up to warn me if there are any SMART errors, and then give me an alert. It will let me ignore it but what may happen is if I wait too long it may not boot anymore or show up if it fails outright. It is an early warning mechanism - not an override. Think of it as a heads up to backup the system, and stop using it if possible.
If both fail, try removing the CMOS battery for 1 minute and hope for the best. If the issue persists beyond these two things, it tends to be a bad motherboard and that will total the laptop out. However, sometimes you get lucky and removing the wireless card helps.