iphone not syncing with iTunes since upgrading software

Hardware:
macbook pro, purchased in July 2008
iPhone 3G, purchased in August 2008
Two knock-off iphone USB connection cable (purchased on Amazon for $2 each)

Software:
Latest iPhone firmware (non-jailbroken)
iTunes 8.1.1
OSX 10.5.6

Symptoms:
Everything was working fine (even with the knock off cables) until I did a recent upgrade of both iTunes and OSX. Now things seem to have gone awry:

1) Yesterday, I had all kinds of trouble getting my iphone to start charging with my laptop. After several attempts it connected, synced, and I was able to get a partial charged.
2) Today, I continue to have problems

a) connect to laptop, wait for phone to get enough juice to start syncing
b) phone beeps, itunes comes up, iphone says "sync in progress". itunes says it's syncing
c) I then hear the camera sound effect (as if I hit the power button). itunes stops syncing with iphone
d) after a few seconds, iphone start syncing again, another camera click noist, iphone says "backing up iphone". Everything seems fine. Backup seems complete.
e) after another minute, iphone starts syncing again. says sync is complete
f) iphone starts syncing again, then stops again. Everything looks fine (except that it keeps resyncing over and over again)
g) after another minute or so, the phone shuts itself down. Pressing the power button does not do anything. iTunes doesn't display the iphone in the left sidebar.

Oh, I forgot to mention that one time when connecting the iphone to the laptop, I got this nasty looking message:

"iTunes could not be connect to the iPhone ** because an unknown error occurred (0xE8000065)"

This message does not occur all the time.