My desklamp turns on my computer

Wow, thats a cool trick.

Check/replace your surge protectors. If you have one, use an outlet tester to see if the ground is working or not. Try changing wall outlets as well or using an extension cord from another room. Try to narrow it down.

Go into your bios and check your power management settings to see if it says anything about "Power on after power outage" that sort of thing. Turn off anything that automatically turns on the computer.

Also, how old is your house.

It is both a home wiring problem and a computer power supply problem, OR an EMI issue.

A. Not too important: The electrical load on the circuit should not be so heavy as to cause a voltage spike or sag. Though that might be caused by the outlet itself if the receptacle is old or worn worn. The lamp may be arcing where it plugs in or at some point in its own mechanical switch wiring.

B. More importantly: A good computer's Power Supply should always have Active (PFC) Power Factor Correction. If the power supply was of this type and good quality, then power fluctuations would not carry over into the computers Wake on LAN or other wake up responses. Even if you have a cheap power supply, having a UPS with Active Voltage Regulation would also block power spikes from reaching your pc as well as preventing power spikes, sags, and outages from interrupting your work.

C. Randomly possible EMI issue: Do you have a wireless keyboard or mouse? It is possible that the lamp leaks so much electromagnetic/radio interference as to cause the wireless signal to shift when it is on. So that the normal field shifts back even when it is turned off. I had a 1955 Case Tractor that produced such an EMI field that the TV image in the house and wireless network would pulse in and out if you drove past the window.