Sounds like a function of the BIOS/UEFI to either skip or silence POST messages (Memory check etc.) If you have a UEFI motherboard and Windows 8-10 you may have a "boot to bios" option in advanced boot options under Windows. You should be able to find this under the metro version of settings which you can access from the start screen. (Just type "boot" on the start screen and you should see it)

If it's an older laptop with an actual BIOS then you are going to just have to try hitting various F keys on boot. Try holding the key down before you hit the power button...often times the BIOS screen will get mirrored out of the display port... but not HDMI necessarily. So if you have an RGB port and cable, that would be your best bet.

If the laptop has HDMI output, Windows should detect the display when its plugged in and let you switch the output monitor with Windows + P

I replaced my own screen not too long ago and found that you can get most panels for 80$ or less. Replacing one won't require disassembling the whole laptop. Take the screws out from the front bezel then gently lift the bezel around the screen until you feel it pop off the clips. From there it's (usually) 8 screws to remove the back and 4 screws to disconnect it from the hinge mechanism. Then there's a tiny little plug on the back... but there's a ton of Youtube videos showing the process.

Word to the wise.... try to replace your panel with the manufacturer's panel. I've found that the ones that come from "laptop screen" sites are usually pretty poor quality and tend to have a lot of light bleed which washes out dark colors. Some of them also are not shielded well and this can really mess up your wifi performance (the antennas are in the lid right behind the panel.)

Are you using UEFI (not legacy) + secure boot (this is not the same as a password) + win 8/10? AFAIK the fast boot option only works under those conditions