I have the same issue with a 1990 Toyota Camry ...

Sounds to me like you have a bad battery, or corroded battery terminals, or the Universe doesn't want you driving on Thursday nights.

If your battery is the original one, it is probably getting very weak (that's 13 years old). Batteries last approximately 4 to 6 years then loose potential rapidly from that point on. If that is not the case, then you have a short somewhere in the wiring that is draining the battery.

Follow the wireing loom from the alternater bending in several places while someone is watching the light. I found the samething on someones camry before. A broken wire along the intake manifold in the harness

the battery seems to be surging
Huh????

Try typing year and make of car then fuel pump relay location into Google images, hopefully should be a pic of where it is.

The battery has seen better days wear gloves and eye protection in dealing with it. The alternator should be checked out. Get a NEW battery and put a voltmeter on the terminals and start the car. Voltage should be between 13.5 to 14.5 w all accessories on. Anything over this means the voltage regulator in the alternator is shot. Remember you can't test the alternator with the old battery ITS DANGEROUS. Batteries can short out especially if they are overcharged. You probably have a sulfated battery which means that its ability to accept and give a charge is destroyed . Therefore the battery is useless.

Your alternater is over charging the battery. Either the alternater is faulty , or just the regulator. Also, check the positive cable from the battery to the starter, and make sure it's not shorting out somewhere.

Ok you have a main fuse that is blown. Or maybe a fusible link.

need alternator replaced or refurbished

You need to take this to a dealer, I think you may have an issue with the injector circuit, possible a defective PCM or wiring issue to the injectors, I don't think that the injectors themselves are the cause.