Almost dead: no screen, no sound, still syncs

Very suddenly my iPhone 3G stopped working in many ways, but still appears alive to the computer when it's plugged in. I want to assess my odds of doing a successful repair, so I can weigh whether to try to fix it, or put away the same money towards a replacement.

Things that are broken:

-Screen is black, no display of any kind

-Does not go "glink" when usb cable is attached with power.

-No ring or vibrate when i call it from another phone.

-No vibrate when flipping switch from non-mute to mute.

Things that still work:

- When I call it from another phone, it seems to ring the usual amount of time instead of going straight to voicemail. That's what i hear from the other phone; nothing perceivable happens at the iPhone.

- When I attach it to my computer, iTunes sees it and I can successfully sync.

- iTunes shows battery level on phone, and it appears to charge over time.

Phone condition:

- Rough. Back severely cracked in multiple places, but no recent drops.

- A couple times recently when trying to sync, I have received an error about not being able to sync apps because it couldn't determine which apps were installed (?!). Restarting iTunes seemed to resolve that error.

- I spilled water right before it went dead to me, while phone was on me. I honestly don't think any water could have got into it, but it's suspicious because it happened so close to the problem.

What should I try, and what are my hopes? Is there a single bad connection inside that could explain everything?