You're using the stock, 8.4 nimah batteries? If so, that , slightly discharged batteries and not enough of a trigger pull is the combo you're getting , it's pretty well known for stock tm recoils.
I suspect if you switch it to full auto rather than smacking it then it'll start as well. Essentially what you have is exactly what you're describing, not enough juice is getting to the motor to turn the gears enough and it's stopping just before firing (used to be referred to as lock up).
Normally, you're absolutely right to run it stock, a TM especially however this is one of those things that are just crap. The stock batteries are crap and there is no recouping your money for them. My advice would be to buy some 7.4 lipos and use those, You'll either need to convert the rif or buy a converter. IF you can solder 2 bits of wire together, convert it yourself, there are videos (probably from eagle6) on how to do this on youtube. It's easy if you can solder.
If you can't solder or are too intimidated to, then some retailers (I think fire support do) that sell a converter.
There are other methods to solve this. You can try really hard to give the trigger a good pull every time, however the batteries likely aren't up to the job, they were probably sitting in the retailers inventory for years, so while they might be new to you, they could be 5-10 years old. You can fit or have fitted a mosfet, the Gate Titan is the current one, this is somewhere in the region of £100-£170 (depending on model) plus labour (been a while since I looked), but it is pretty awesome. If you're doing this and paying someone to, then I'd consider a spring upgrade too, even if just an m95 or m100 as this is a gearbox open job.
Where abouts are you based?