Board broken, so how to connect a usb cable directly to the board?

First of all, double check that you can't peel your data off via Bluetooth. Or maybe it charges through the microUSB port and the battery is flat?

From your description it sounds like the USB socket has lifted the tracks from the board, which may make it very difficult. In any case, you'll need to do some very fine soldering using an iron with a fine 1mm or less tip. Here's a suggestion that may or may not work. Checking on eBay I found a male to female micro USB extension lead. Get one of those and chop it in half. Strip an inch or so of the outer sheath of the female end to expose the 5 wires, which, with great care, you may be able to solder to the board. Google for "micro usb pinout" for the colour coding of the wires. Get a flux pen and use it to add extra flux to the tracks and the wires before attempting to solder.