Can a cathode tube light be run off a battery?
****WARNING: The tube drivers decsribed below make a very  higher voltage to operate the tube. Hundreds of volts is typical. Over 1000V occurs on large CCFL units.
 You can get a serious electric shock from these.**   


**If you do not take enough care you MAY die.**** 


I assume that you mean CCFLs "Cold Cathode Fluorescent Lights".
 Like these - 



IF they ran from the 12V from  a SATA power plug you can run then from 12V. If so they will have had a controller which must be used with them. The controller converts the 12V to a higher voltage.

They may have run from the STA 5V supply - less likely. You need to connect to a SATA power supply socket and measure which voltages appear where ON THE INPUT TO THE CONTROLLER FROM THE SATA SOCKET. Do NOT try and measure the output voltages from the controller. Cheaper meters may emit magic smoke and meter users in some cases may emit magic smoke as well. 

Useful CCFL page

CCFL driver IC datasheet - UCC3973 etc - shows what's involved. You do NOT want to build one of there. Commercial units are cheapish.