I had the same problem and soldered it back no problem. Worst thing that can be done is you'll break the flange things holding the plastic around the thing.
Also, I think i may have a numpad sitting somewhere in my shed, so you may see it go up on ebay sooner or later.
One final though is to do the five finger smack.
Worked all the time on my non responsive numpad.
Other unforseen problems you may face:
Too much solder = bad covering too many connections can be troublesome.
I literally put a pinhead sized drop on a pin and heated with a creme brule torch.
I'd offer to do the repair, but mine is TOTALLY functional, but horrible looking. Clear plastic tape holds my plastic covers together. And an old mousepad glued to the bottom.
I think i may have used my teeth to strip the wires too.
I thought I posted picks of all the ghuts on the numpad when I took it apart. I'll try to find them again and re-port.
Good luck with it hope you get it back in working order.
Found my post with the repair:viewtopic.php?f=16&t=328&p=1720#p1720
Again good luck with it.