Horn is constantly blarring
 

Hi guys
Iv got an 05 mazda 6 he car was sitting in the drive for a week or 2 and outta the blue the horn started going off this happened when we where out so the horn kept going until the battery died. After charging and reconnecting the battery the horn was still blasting
So disconnected and took the horn relay/fuse out, reconnected the battery again and the alarm went off for mabye 30 secs then switched itself off thought I better let it run for an hour or so to make sure the battery was charged properly then gave it another go with the fuse and it worked no blarring horn I then went to test the horn 1st beep fine 2nd beep got stuck on again. Need to get through an mot so gotta fix it any advice?? Also the car outline with key inside is on in the dashboard but I switch the headlights on and it goes off?? I have reprogrammed the keys but light is still on?