It is a model PA-21 charger. I have tested it in another laptop to make sure it charged properly and it shows a steady green light on the brick.

Could a broken ZIF connector between the system board and the power button be an issue? It didn't seem to stick well for either of the small ribbon cables for either the power board or the touchpad.

You "tested the power cord/adapter" how?

What model/part numbers are on the Adaptor?

So you have one of the laptops with the Octagonal connector on the dc power cord end.

NX061     DELL XPS series (M1330, M1530 (PP28L), M1540), Inspiron series (1318, 15., 1545 (PP41L, 157B) ) Dell original ac adapter, 19.5v, 3.34a, 65w, PA-21 family, OCTAGONAL tip, numbers on part may include 0NX061, LA65NS2-00, PA-1650-02DW

Dell™ Inspiron™ 1545 - Documentation

The power board can be damaged by improperly removing the flex cable.

However you say that the system works with the battery installed.

So that would indicate to me that the power input connection on the motherboard is broken.

The laptop should run when the battery is not connected or installed in the system.

Removing the Power Board

1. Follow the instructions in Before You Begin.

   <ADMIN NOTE: Broken link has been removed from this post by Dell>

    
   
   
2. Remove the center control cover (see Removing the Center Control Cover).
   
   
   
3. Remove the keyboard (see Removing the Keyboard).
   
   
4. Lift the cable connector latch that secures the power board cable to the connector on the system board and remove the cable.
   
   

NOTICE: Be extremely careful when removing the power board. The power board is glued to the computer. Do not pull on the cable to loosen the power board.

1. Use a plastic scribe or screwdriver to pry the power board off the computer.
   
   
2. Lift the power board off the computer.
   
   

System Board

Dell™ Inspiron™ 1545 Service Manual

  Removing the System Board

  Replacing the System Board

CAUTION: Before working inside your computer, read the safety information that shipped with your computer. For additional safety best practices information, see the Regulatory Compliance Homepage at www.dell.com/regulatory_compliance.

NOTICE: To avoid electrostatic discharge, ground yourself by using a wrist grounding strap or by periodically touching an unpainted metal surface (such as the back panel) on the computer.

NOTICE: To help prevent damage to the system board, remove the main battery (see Before Working Inside Your Computer)   before working inside the computer.

NOTICE: Only a certified service technician should perform repairs on your computer. Damage due to servicing that is not authorized by Dell™ is not covered by your warranty.

The system board's BIOS chip contains the Service Tag, which is also visible on a barcode label on the bottom of the computer. The replacement kit for the system board includes a CD that provides a utility for transferring the Service Tag to the replacement system board.

NOTICE: Handle components and cards by their edges, and avoid touching pins and contacts.

Removing the System Board

1. Follow the instructions in Before You Begin.  

    

   
   
   
2. Remove the hard drive (see Removing the Hard Drive).
   
   
3. Remove the optical drive (see Removing the Optical Drive).
   
   
4. Remove the center control cover (see Removing the Center Control Cover).
   
   
5. Remove the keyboard (see Removing the Keyboard).
   
   
6. Remove the base cover (see Removing the Base Cover).
   
   
7. Remove any installed memory modules (see Removing the Memory Module(s)).
   
   
8. Remove the processor heat sink and processor (see Removing the Processor Heat Sink and Removing the Processor).
   
   
9. Remove the display assembly (see Removing the Display Assembly).
   
   
10. Remove the palm rest (see Removing the Palm Rest).
    
    
11. Remove the daughter board (see Removing the Daughter Board).

    <ADMIN NOTE: Broken link has been removed from this post by Dell>

    
    
    
12. Remove the four screws that secure the system board to the computer base.
    
    

1. Disconnect the thermal fan cable, speaker cable, and USB board cable from the respective system board connectors.
   
   
2. Lift the system board at an angle toward the side of the computer and out of the computer base.
   
   
3. If required, remove any installed Mini-Card (see Removing the Mini-Card).

I have tested the power cord/adapter and it is definitely working. If you meant the actual charging board with the power jack on it, I have just installed a brand new one. That might be a problem, but it would mean I was shipped a faulty board. Any ideas on how to test it?

The system should run without a battery.  The adaptor may be bad.

It does not work with the battery in, it flashes the 4 Amber Lights, 1 White light on the power LED when the battery is in. No matter how I have tried to turn it on, it will not. It only shows lights when the battery is in, but will not boot.