no clicking, no dragging starter, zero audible ..nothing re 1992 Corolla sedan

I have been clutch-starting my auto for a few weeks now (guess what?; that won't always work on an icy/snowpacked road !) ; I put a new
battery in in November ; about 6 weeks ago i tried to start after shutting it off for 15 minutes and there was nothing when the key was turned --- 10 minutes later it started quickly.
The identical thing happened again, but just a week later. The incidences iincreased til it was every day, eventually became every time I tried.
I have: cleaned wire connections at starter/solenoid and at battery I have not replaced solenoid; how do i know if i possibly need a solenoid or if I need my starter rebuilt ? Are there kits sold to rebuild toyota starters ?
Will a mechanic rebuild the starter or tell me to buy one rebuilt/new and make dollars off that whole process ?
thanks for any advice one might have to offer
omaha is hilly but not everywhere to pull off a clutch start .... thank you
roadwarrior
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I'd check or change the starter solenoid myself...
--

-Gord.
(use gordon in email)
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Did you remember to check both ends of the negative battery cable as well ?
Asbjrn.

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