A black screen is scary because it looks like the PC is dead, but if the fans spin and you hear it boot, the machine is alive — it's just not drawing a picture. That narrows things down a lot: the problem is either the output path (monitor, cable, graphics) or a loose part (usually memory).
Work down this list in order. Each step takes a minute or two, and together they cover the overwhelming majority of no-display faults.
Before you touch anything
Listen and watch carefully at the moment you press the power button. Do the fans spin? Do any LEDs blink in a pattern? Is there any beeping? Those clues matter. If the PC doesn't start at all (no fans, no lights), that's a different problem — it's power, not display, and you should look at the cable, the wall socket, and the power switch on the back of the supply.
Step 1 — Confirm the monitor is alive
Press the monitor's own buttons (not the PC's). If you can get a menu or change the input, the monitor is working. If the monitor does nothing, it's not getting power or it's off — check its own cable and socket. A dead monitor is the most common cause of 'my PC is broken.'
Step 2 — Check the video input
Monitors have several inputs: HDMI, DisplayPort, DVI, VGA. If the PC is plugged into HDMI 2 but the monitor is set to HDMI 1, you'll get a black screen. Use the monitor's buttons to select the input the cable is actually in, or set it to Auto if it has one.
Step 3 — Reseat the video cable
Unplug the video cable at both ends and plug it back in firmly. Try a different cable if you have one, and try a different input on the monitor. If you have a desktop, make sure the cable is plugged into the graphics card at the back, not the motherboard above it (unless you have no graphics card — see below).
Step 4 — Reseat the RAM
This is the fix for a surprising number of no-display PCs, especially after moving or bumping the case. Power off, unplug it, open the case, and take each RAM stick out and back in until it clicks. If you have more than one stick, try them one at a time in a single slot. A single bad or loose stick will stop a PC from ever reaching the display.
Step 5 — Check the graphics card
If you have a separate graphics card, make sure it's fully seated and its power cable (from the supply) is plugged in. Remove it, blow out the slot, and reinsert it. If you don't have a separate card, your PC relies on the graphics built into the processor — in that case the cable goes into the motherboard.
Still black?
If you've done all of the above and the fans still spin but nothing appears, the fault is more likely the motherboard, the power supply, or the CPU. At that point a local technician or the PC's warranty is the sensible next step — chasing it further usually costs more than it's worth on a typical home machine.
A useful test: if the monitor shows its 'No signal' message, the monitor and cable are fine and the problem is inside the PC. If it stays black with no message at all, suspect the monitor or its power first.