When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.
These cars do funky things when the battery is going. Focus on the battery and getting the car started then look at those other issues if they are still present.
Even if battery voltage checks out OK, corroded cables are a known issue. I think the TPMS message is a red herring--it's also common and shouldn't have any affect on starting.