Lexus Troubleshooting Questions? Ask a Lexus Expert
Hello and thanks for using the site. If you can "jerk" your negative cable then there is a loose connection at one end either the battery or where the cable is grounded to the body. I would inspect both ends for corrosion and clean and tighten them. Please let us know if replacing the cable worked for you. I would also have your battery tested while its disconnected just to make sure the cells and amperage output are good.
Your welcome, yea there really is not anything else to bother looking at right now if jerking the cable fixes it then the cable, terminal connection themselves. I forgot to note your brake pedal, but the pedal only becomes stiff due to pressure buildup from pressing the pedal before the engine provides the vacuum for the system so there is no concern there.
Have you gotten a chance to replace the cable yet?