What frame does my mountain bike have?
You  probably will waste more time trying to identify the bike compared to just replacing the BB. 

Two options - Easy but likely more expensive - take the to a bike shop have them supply a BB of the correct size, if they supply the wrong size, they should be prepared to swap it. 

Or buy one cheap off the internet (probably 68x115) and if its the wrong size, well you have a spare the wrong size for you current bike. 

Its unlikely a spindle length of a couple of millimeters too short or long (i.e. one size up or down) will make a major difference. The worst happens is the front derailleur rubs when cross chaining. BB are cheap - $10 for a cheapy, $20 will get a reasonable quality one for that bike. So it won't break the bank if you buy the wrong size first time.