Lights on dash, drive,park, reverse, etc flash after starting car

the engine must crank first or you engine can never start.
so is starter failure path only, not the engine.
well the car has an automatic transmission
the PRNDL switches (shifter) allow cranking in park or neutral
so try to key crank the engine in Neutral, as the users guide tells you.
1: battery lugs clean and tight
2: head lamps bright ,key on or key off?
3: dash blower sound good heater blower on high key on/?
4: jumper cable starting work, all tow truck drivers to that and do so safely not backwards and blow things up,.
5: test the battery in shop with load tester
6; charger the battery first before #5 test.
7: replace, starter relay
8: hot wire starter to prove it is good.?

if the 8 things confuse you ,do like 99.9% do, they get the car repaired.(in a shop)

my car can be push started but not yours if A/T box

Yes you must have a Honda Accord. Or civic.

of course changing a brake pedal switch will not help in a reversing light problem
they are two totally different circuits
check for a damaged wire at the reverse light switch or bulb holder for the reversing bulbs for a dead short
as for the rest check the IGN fuse under the bonnet

First thing I would check is all frame grounds... like the negative battery cable and the grounding strap on the passenger side motor Mount to the wheel hub. In any electrical system, lights draw more current than anything (except the battery) when you turn them on... Check the grounds!

check all fuses under dash it mightt be a switch though

the switch that makes the light change from P,R,N,D etc...is faulty and needs replacing it should be around the T bar area under console as the lights on the dash are controlled by a switch

The lights have nothing to do with your car not going in reverse. I know this is going to sound silly but, are you releasing the parking brake? That brake is the lever between the front seats. Are you taking your foot off the brake?

I know they sound silly but you would be surprised at how often this happens with th eparking brake.

When you put the car in reverse can you feel the transmission engaging? You should feel a slight **** when you put it in reverse with your foot on the brake. If you are not feeling this, your transmission needs to be repaired.

may have problem in distributor

it does sound like the switch has the problem and i wouldnt recommend trying to fix this yourself unless you are mechanically enclined to do so.it shouldnt cost very much money to have a professional do this for you.

WILL THE CAR START AND DRIVE