Electrical

Exactly which lights turn on? If they are all related to safety systems like ABS and air bags, those are run by computers. Computers do weird things when system voltage is low or unstable. When multiple computers are involved, the charging system and battery are the most common suspects. I would start with a charging system test, with particular attention paid to full-load output current", "ripple voltage", and charging voltage. Most professional testers only list ripple voltage as "low" or "high" on a relative bar chart, which is fine.

If the original battery is still in the car, that is also a good suspect, even if it starts the engine just fine. Due to the way little electronic voltage regulators work, they cause the generators to develop huge voltage spikes that can damage the internal diodes, and voltage regulator, and interfere with computer sensor signals. The battery is the key component in damping and absorbing those spikes, but as they age and the lead flakes off the plates, they lose their ability to do that. Those spikes can cause computers to become confused.