How do I sync my iPhone to my new Windows computer?

(My iPhone syncs fine with a bunch of other computers.)

iTunes won't run after installation.

I Download iTunes from http://ift.tt/LvhEkp

The installation goes without a glitch.

When I run it it says "Apple Application Support was not found. Apple Application Support is required to run iTuners. Please uninstall iTunes, then install iTunes again. Error 2 (Windows error 2)" (I get this message twice, with one minor variation. The advice does not help.)

I found articles on the net (http://ift.tt/1v2fiHj) which says to use WinRAR to unpack the installer and then install the components one by one.

Download and install WinRAR.
Right-click the iTunesSetup.exe icon and choose "Open with WinRAR".
Once the EXE is opened in WinRAR, double-click AppleApplicationSupport.msi and when the installer window is open choose "Repair".

iTunes now starts fine.

I connect my iPhone 4S. Nothing happens. It is not charging. iTunes does not discover it.

There is a message about "USB Hub Power exceeded." This happens regardless if I connect it directly or through any of my three (3) different externally powered USB hubs.

I had this before for USB Memory sticks as well, but re-installing drivers helped.

What do I do now?