My laptop HDD is broken, is there any way I can connect my other desktop PC to It?

My laptop HDD is broken, how can I use it using only the monitor and the keyboard but the hardware of my other desktop computer pluggin it via HDMI?

You can't. The laptop's HDMI port is not designed to receive HDMI signals, and even if it was, it would most certainly need some sort of capture software to capture the signal and show it on the laptop's screen.

As for the keyboard; without some weird HDMI tricks, custom hardware and a custom driver, it would be impossible to get a keyboard signal to go over HDMI. HDMI was designed for audio and video (some control signals+ethernet), not for USB devices.

You can get a lower performance option in form of a thin client archecture if really only the hard disk is broken. Boot an operating system from a USB key (like Ubuntu Desktop) and use an RDP/VNC client to control the desktop computer.