Some computers require you to toggle the monitor function key in order to enable a monitor on the external monitor port. I usually disregard what happens automatically when I plug one in. Often the external monitor button will cycle between the built in monitor, an external monitor, both, and back to built in.
Sometimes even a TV will work as an external monitor.
The other path is to press F1 ( or F2 on Compaq motherboards), which will give you several boot options. One of them is usually 'safe mode'. One manufacturer, I think Toshiba, needed F6 IIRC...
I keep a note on my phone with all the boot options on my various computers over time.
Here is a summary that includes those
@Dabbler listed and a few others.
Common keys used to access the boot menu include
F1, F2, F3, F5, F8, F11, F12, Esc, and Del. When you turn on your computer, pay attention to the screen for any instructions or prompts that tell you which key to press to access the boot menu.
Sometimes you have to repeatedly press the key during startup. Sometimes you have to hold shift while you press them.
Usually, you have to do it before the logo shows up, sometimes afterward. And SOMETIMES during a short time slot window. Patience rules.
A few computer makes have a dedicated key, and I've seen one that can be accessed even after the computer has booted.
If all else fails, google your computer model and "boot" and "restart". Eg "Asus k1220 laptop boot restart"
The old way of accessing the data on a hard drive sucks........ I have a kit I use that allows me to access the various drive technologies. I'm usually in a very bad frame of mind when I grab that box......
Good luck John.