Takeuchi TB125 starting problem

I have a 1999 TB125 with a starting problem. When you turn the ignition key to the on position after about 2 or 3 seconds it starts with out turning to the start position. This problem started about 3 months ago and I just let it go because it didn't seem like there was any other issue. By that I mean it didn't sound like the starter was constantly ingauged or any other noises and it ran fine. Yesterday after PM'ing the machine I could smell an electrical burning smell afterstartg and running/itleling for a little while. After investigating I found the odor coming from the starter/silinoide and it was hot to touch. After explainig this to the Takeuchi dealer/repair shop they advised I needed a new starter and should replace the ignition switch at the same time. I replaced both and the problem still exists, but now when it starts I can hear the starter staying engauges, so, of course I shut it down emediately and tried this a few times. I asked the shop if there was anything between the ignition switch and the starter that could be causing the problem. They said there was nothing. There has to be something, there is a delay between turning the key to the on position and the machine starting. Can anyone help with this issue?:Banghead:Banghead:Banghead:Banghead:Banghea d