It sounds like you might be running in compatibility mode.
Option 1
1) Slide your finger in a downward motion to try reaching the password field
Option 2
1) Go to Options>Applications
2) Highlight Google Sync
3) Press Menu>Disable Compatibility Mode
4) Run Google Sync again
5) Try just clicking in the Password field now.
I had similar issues with another app while the "auto-complete" option for typing was still enabled. Try to set it back to "auto-correct" and see if that helps.