Hi
Can you provide the specific model of CQ60 Laptop, see How do I find my product name/number? if you need help finding the specific model number.
First I would just try a hard reset: see Performing a Hard Reset or Forced Reset for details, the only change I would make, is that in step 7, don't reinstall the batter, and see if the notebook will power on with just the AC Adapter connected.
If the notebook will power on, then definitely go and update the BIOS to the most recent version for your model. If I had your specific model, I could post a link to it.
If the notebook still doesn't power on or respond at all, check out Troubleshooting No LED Lights Glow During Startup or Boot for some additional troubleshooting steps to try.
Good Luck!
R