I'm usually way off base on things but I'll throw this out there anyway. I, too, have a 2004 BX23D and have had starting problems from time to time. My neighbor helped me at one point when I couldn't get it started for many days...the starter cog wheel had not retracted. With a long-handled screwdriver, he pushed that back in and it started without another hesitation.
But...starting problems returned. I tried the screwdriver push back and it helped at times but not always. I even have purchased a starter but hadn't installed it since the problem was intermittent.
Then, I discovered what may be the REAL problem. The speed selection lever wasn't easy to move between "turtle" and "rabbit" when the tractor hadn't been used for a few days. When I thought the transmission was in neutral, it really wasn't. In looking down into the area where the selection lever goes into the transmission, it appeared to be quite dirty. (The last owner was negligent in most areas, including keeping things as clean as possible.) If I had taken the right wheel off, I could've accessed the area more easily but I didn't want to go through all that. So, with a rigid wire, screwdriver, anything that would help clean the area, I was finally able to get the buildup broken away. Then, I sprayed with White Lithium grease and worked the lever many times. Result? Started right up.
Now, once I am ready to shut off the tractor, I make sure the speed selector is moving easily from the slow to fast. And, prior to starting again when the engine is cold, I move the lever to both speeds to make sure it is in neutral. So far, it is working. And, with continued use, thanks to the Lithium grease, the movement of that lever is working much better. Strange thing was...when the engine was running, there was no problem with moving that lever to either speed. Go figure.
Anyway, check you speed selector lever to make sure you are really in neutral. It would be interesting to see if it could be the same problem. For a 20-year old tractor, I have no complaints about this baby. I hope you feel the same way about yours...well, after you get the problem resolved anyway!
Tractor Gal