If you're lucky the power button hasnt snapped off from the solder lugs, from there i suppose you could remove the plastic power button and put the tablet back together and hit the button with a pencil or something and get into recovery. Unfortunately i have had 3 of these buttons break on 3 separate tablets and every time for me the power switch has completely broken off from the PCB, so data recovery was not an option.
And Lenovo, for whatever reason has deemed it easier to replace the whole mainboard by default (the power board itself is not connected to the main board at all) and upgrading you to the unrootable OTA version. and giving no option to retain customer data. though they seem to be pretty good about preserving data on Laptops and dekstops. so even if you have a nandroid backup theres no way to restore it because you cant install CWM! and no way to run any good backup software on the tablet without root! Lenovo completely lost my respect. since i lost a hundred or so hours worth of work my tab (sketchbook adobe suite) has turned into a bookend, I really hope you are able to make a backup and if not hopefully you get to keep your data, and hopefully all my bitching and complaining towards lenovo will help somebody out
Motorola Photon - CM9 - Beta
Lenovo Thinkpad Tablet 64gb 1839 - Stock, Rooted!, CWM
Barnes and Noble Nook Color - Phiremod 6.1