My HP Desktop has power but it will not turn on

[Julie156]

The light on the back of my monitor is on which suggests it has power, however when I push the power to turn on it does nothing 

[itsmyname]

@Julie156 -- that lamp signifies that the power-supply is receiving power.

It does not guarantee that the power-supply is sending a few different voltages to your various components.

Is your computer an "All-In-One", or are the computer-case and the monitor two separate items?

Any All-In-One is very-difficult for a computer technician to try any "part-swapping" to try as an attempt to revive it.

If a "desktop" computer does not start, the "usual suspects" are:

1. a broken on/off button
2. a failed power-supply
3. a failed processor
4. a failed motherboard

I recommend that you take your computer to a local owner/operator computer store, and first get them to experiment with a different power-supply.  If that resolves the issue, purchase that power-supply. They will probably fully install it, for a small service-charge -- $20 to $30.

Otherwise, they will need to do more-extensive "trouble-shooting".

Set an upper-limit on what they will charge you for their efforts, to avoid any outrageous charge.