I had this issue as well. It's not a short to ground; it's a common problem with that radio. The only solution you will find is to send it in for repair or replace it. It is a relatively simple job.
All I did was purchase an after market radio (about $100) and an in-dash adapter (about $75) and then sold my non-working radio on ebay for $15. Someone out there buys them, fixes them, and then re-sells. Apparently it's a series of bad electronic components causing the problem with the Alpine radio head.

Here's how I did the job:
- Purchase new aftermarket radio (I chose one with blue tooth and USB capabilities for ipod and MP3 capabilities)
- Purchase factory integration adapter from Crutchfield (Honda Accord Factory Integration Adapter Factory stereo integration adapter for 2003-up Honda Accord with heating, ventilation, and AC controls at Crutchfield.com) I got it for 1/2 price because I also bought the radio from them.
- remove old radio according to these instructions: How to Replace the Radio in a 2003 Honda Accord EX | eHow.com

I didn't use a trim tool to remove the vent assembly; instead I cut a piece of hanger wire about 8-10" long and then bent it to a "U" shape. On each end of the "U" I bent outward facing hooks. Then I inserted this tool into the vents and grasped the inside of the vent with the hooks. Then I gave the tool a quick tug to release the assembly from it's hold-down clips. Once released I had access to the top bolts on the radio. Everything else is as described in the web link. Good luck.

 

I am having similar issues. Started about a year ago when the cd player just quit. About a month ago, it came back on and finally discharged all the cds(including one from the library). In the last week or so, while driving it occasionally seems to lose power (dashboard lights flash, radio cuts out, dash lights all illuminate, etc). It doesn't happen everytime and today it happened 11 times in a 6 mile drive.

Is this a problem I can solve myself or does it need a Honda mechanic to get to the bottom of it?

 

same issue for me as well. if you pound on the display a few times it comes back. LOL i only resorted to this madness once i made my mind up to put in an after-market unit...which is awesome! btw, my cruise stopped working as well. thought of a ground issue but didn't want to pay an arm and leg to someone to figure out.

i'll be interested to know if someone figures this out.

 

I had similar problem.....took radio unit out of the dashboard....removed oxidation and re-soldered cold joints in PCB....and it is working well