Fixing after saltwater exposure

Have followed the posts here carefully but they are not answering my questions.

1. iPhone 3G was dropped very briefly in salt water and then appeared dead. Would not turn on.

2. Took it apart and followed all cleaning directions here except did not remove logic board heat shield.

3. Plugged phone in to AC power and got a bright display with black background and white apple logo, so it is obviously able to begin boot process on wall power.

4. After 2 minutes of "booting" the apple logo gradually fades to white and the unit dies. If you turn it off and on again, this sequence will repeat.

So I have three questions...

5. Seems pretty obvious that I need to next soak the logic board in alcohol as others suggest here. Does the progress from non-functional to partial boot-up seem like I'm making progress or is there some potential "fatal" thing causing boot failure?

6. Is battery involved in booting the iPhone-- so that replacing the battery makes sense EVEN THOUGH I am powering from the wall socket and it still isn't getting past the apple logo?

7. iFixit does not seem to sell iPhone logic board replacements. Is there a reason for that?