Why after replacing the alternator and checking all wire connections is the dashboard battery light staying on?

easy to see why
starters do not charge batteries
alternators do that

The alternator won't work without battery voltage at the connections on the alternator . The heavy gage wire on the back needs B+ voltage . The connector on the front of the alternator , how many wires ? What year , make , model vehicle ? Could also have a smart charging system , controlled by the PCM/ECM - engine computer > You may have wasted your money buying a new alternator an battery .

Brother Mark, changing the battery with a new one being done won't make the light go out, as you noticed. Light is still on so you changed the alternator. Good, but the battery light is STILL on. This only means that the charging circuit from the alternator is not working in the voltage regulator or the wiring is not connected properly to the alternator/regulator. A new battery will show over 13 to 13.5 volts not connected. An old battery will still show 12 volts and still be weak or bad. After connected and engine running, the system will show at least 14 volts because alternator/regulator is working properly, using a voltmeter/load tester connected to the battery. If after replacing the battery and alternator it is still reading 12 to 13.5 volts, it is not working and the light will stay lit on the dash. You may have purchased a faulty alternator if the system tests out this way. Have your system checked with a volt meter or load tester bit be sure all the connections are proper and clean.

if its not in the wiring/connection behind the dash cluster, the control module may be haywire..

There are two things that generally cause a battery warning after an alternator replacement. The most common is a loose connection either with the control plug (aka “relay” plug-in), charging line connection, or the ground. The other is a blown fuse or defective connector or relay, which could have been broken or shorted when the alternator was installed or on the first start-up after its installation.
You can check that the alternator is supplying enough power by starting the car and disconnecting the battery. If the car dies, the alternator isn't working properly (or a wiring/relay/fuse issue).

CHECK ALTERNATOR DRIVE BELT COULD BE LOOSE NEED ADJUSTING OR GLAZED NEED REPLACING. IF ALL IS GOOD, CHECK ALTERNATOR VOLTAGE OUT PUT AT BATTERY SHOULD BE 13.5 - 14.5 VOLTS. IF NOT ALTERNATOR FAULTY BUT CHECK ALTERNATOR BATTERY FEED AND VOLTAGE REGULATOR WIRES FOR LOOSE CONNECTION OR DAMAGED FRAYED WIRES. CHECK ALTERNATOR FUSE.CHECK THOSE THINGS BEFORE BUYING NEW ALTERNATOR.FIRST TURN OFF RADIO BEFORE DISCONNECTING BATTERY CABLE TO KEEP FROM LOCKING OUT RADIO.

sounds like you have a charging problem, i would suspect the your alternator is not working properly,that is why your battery is not staying charged and also the reason your dash lights are acting funny..check and make sure you have a good wire connection to you alternator and the the electric plug didn't just fall out or is loose..

No not the computer or wiring, when the battery goes out the alternator has to work harder. With a weak battery the alternator produces a magnetic flux the flux need to be disapated. Only a good battery can do that. All you bulbs took on at least 15vlts and are rated for 12(it can withstand 16vlts) the 2 lights on the dash any shop can do that or dealer

most front wheel driven japanese car's fan belts are located on the left side of the car when you are facing the hood.... all fanbelt covers are usually hard plastics.... you wont have a hard time locating it...

its not charging, check the belt that drives your alternator, your fuses, check for some loose connections at the back of alternator, if the light stays on while the engine is running, replace your alternator. good luck!