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The best solution I've found is to use the pellet type bait poison. Place it outside of the car near the wheel well areas. Make sure no pets are around. They may be attracted to the poison as well.
you're having an immobilizer system problem. The small battery you're describing is not the problem. The immobilzer system needs to be checked with Honda HDS type software and compatible hardware. I've also seen high resistance at the ground G101 cause this issue.
EGR voltage at idle should not be higher than 1.21v. If it is inspect the egr sytem further. The idle may just need to be re-learned which is done by letting the car idle with no electrical loads on. Let the car idle until the cooling fans cycle two times. If there is an idle control system failure the car will typically code for P0505 idle control system failure.
2000-3000$ here in Raleigh, NC
It's common for the thermostats to stick in the open position on these engines. Remove the thermostat and inspect it.
If the check engine light is flashing there is a misfire that has the potential of damaging the catalyst.
It's pretty common for the Oil pump or housing seal to leak.
Always make sure the wheels are evenly torqued to 80 ft/lbs during tire rotations. Make sure the brake calipers or slide pins are not sticking. Also,Inspect the front hubs for run out with a dial indicator. If they are not true you'll have a variation in rotor run out.
Cleaning the EGR port passages will be required. Also inspecting the operating and resting voltage readings for the EGR valve will help diagnose the P0401 code.
The V6 model 2003 Honda Accord has a rather high failure rate. If you have it overhauled be sure to install a new torque converter. I'd highly recommend the reman transmission by American Honda.