See if it has a fuse that is blown. Otherwise, you have to trace electricity from the battery to the key switch to the solenoid to the starter.

If the fuse is okay, next step is to check the wiring, particularly from the battery to ground (make sure this cable has good connection to the frame), and battery to the solenoid. If all wiring okay, you're gonna need a multimeter to go much farther. Do you have one, and do you know how to use it? Also, if you know how to do it, you might try jumping the two solenoid posts -- but if you don't know what I mean, then DO NOT make an attempt!

***"I just put a new battery in it"***
Did this problem arise after you put the new battery in? or was the problem the reason you put the new battery in??
If it happened after you put the battery in, you better go back and look real close at the markings on the battery as to whether you have put the battery in a reversed polarity configuration. The markings are: + means POSITIVE post, the cable that connects to this post must lead to the starter or solenoid. - means NEGATIVE post and the cable that connects to this post must lead to a ground surface of the mower frame or the engine case.
If you connected the battery backward and turned on the key switch, you probably blew the fuse at that moment. You might also have ruined the charging diodes or the regulator/rectifier, (whichever yours has).
Double check the way you have the battery connected. OPE batteries are sold in different arrangements of the posts. One style has the POSITIVE on the left side of battery while the other style has the NEGATIVE post on the left.
If you were sold the wrong battery, or you picked out the wrong battery, it would be all too easy to put the battery in backward from the correct configuration (has happened many times on here).