Starter/alternator/grounding issues

A couple months back my avalon started refusing to start, lights would come on with the key, but when i turned it, nothing but a click. after a few tries it would eventually start and run, usually for the day without issue again. After a while it got worse, and I had the battery tested. It was dead. So i replaced it. The car would still click the first couple times but start more readily then it had previously. Fast forward 2 weeks. I go to start my car, it does its clicking thing, then nothing. The whole car just dies. no lights, no clock, nothing. I gave it a minute and it came back on with dimmed lights and the antitheft system (which goes off if the battery is disconnected) goes off.
since then, i have successfully started the car 2x, but after each shut off, the clicking and no start issue returns.
The battery cables are free of corrosion and its a brand new battery. I have seen issues with the starters and alternators on these cars on forums before, however with mine intermittently working, its slightly different. at least to my limited mechanical knowledge.
I have seen starter rebuild kits for fairly cheap online and alternator replacement options that look to be fairly easy with the tools that i have access to.
Any suggestions for what I should try? My next step is checking the negative ground cable on the car side to check for corrosion since the battery terminal ends are free and clear.
Thanks in advance!