Hi all!
My corolla (1992) has been giving me some problems recently with starting and I think its neither the starter nor the battery. Basically, car would start perfectly fine one time and 10 minutes later it wont or it would sit on idle and then just quit. When it doesnt want to start there is no clicking sound from the solenoid but the battery reads that its fully charged

??? I thought its in the connection battery-starter or grounding wire but then I noticed that even when the car is running the headlights and console light would flicker like they are losing power and if i crank it up to higher rpms power is restored and the light is constant again.....and as I said sometimes it would die when idling.
So now I am completely confused ... the last problem almost sounds like an alternator issue but then it must be connected somehow to my car not starting up from time to time - I doubt both alternator and whatever else died at the same time.
Anyhow, if u can give me some advice I would really appreciate it - I have had bad experience with local mechanics so I wonna try it on my own first before trusting it to them.
Thanks!