Hi all,
Forum lurker for a while.  Have a question and issue and didn't see any posts related to this.  If so, my apologies. 
 
TimeCutter SS5000 - Model 74630 - (oh yea it's got some age) just 'thumps' when trying to start and will occasionally attempt to turn over.  New battery, fairly new solenoid, gets a tune-up every year - has been a really good mower.  I'm having an issue either finding the right starter model number (last thing I can change it seems) or an updated model if old model has been superseded.  From perusing the web, I'm seeing 136-7880 and just want to be sure before dropping the funds for it to be delivered. Kawasaki engine on the mower. 
Thanks in advance.

Update to this. 
Changed battery, solenoid and starter.  Still not cranking and 'thunks' when trying to turn over the engine.  Voltage is good.  The 'thunk' is more pronounced than before, but still no dice for a start.  I'm not particularly a mechanically inclined person, but read it could need a valve adjustment.  Thoughts?
 
Thanks in advance.