Test whether it is the Power On switch, or the Power Supply. Since the LAN card bit the dust, you may be looking at a worse problem, though.
Bypass the Power On switch.
If the Power Supply comes on, the problem is the switch.
[One generic ATX Power On switch, that I have found fits many computers,http://www.directron.com/atxswitch.html
If the Power Supply does not readily come on, the problem is the Power Supply.
To bypass the Power On switch, you will be using a jumper wire on the
24-pin ATX main power cable connector.
Looks like this,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain24
(Not necessarily the same color, and isn't located in the same position on your motherboard, as shown in the link)
Processor to the top, Ram Memory slots to the right.
The 24-pin ATX main power cable connector on the motherboard, is to the near right, of the number 4 Ram Memory slot.
In case you do not have the Owner's Manual, for your Inspiron 530 desktop computer,http://support.dell.com/support/edocs/systems/inspd530/en/index.htm
On this page left-click on -
Owner's Manual - View - Download - (HTML 3.44MB)
Left-click on - Removing and Installing Parts
Left-click on - System Board Components
(System Board = Motherboard)
Number 7 - main power connector (ATX_POWER), is the
24-pin ATX main power cable connector, on your motherboard.
Referring back to the Playtool link, you will see a wire with Green insulation on it.
This is the Soft Power On wire. (PS_ON)
A jumper wire is used to connect it to ANY Black wire.
ALL Black wires are Ground wires.
[This is a DC circuit. There is a Positive, and a Negative.
A Ground wire is a Negative wire.
The green Soft Power On wire, is a positive wire containing 5 Volts.
You are completing a circuit.
The Soft Power On circuit.
You are bypassing the Power On switch]
There is no splicing of the wires to connect the jumper wire.
The jumper wire will go down into the socket holes, of the 24-pin ATX main power cable connector.
One end of the jumper wire goes down into the socket hole, containing the green Soft Power On wire.
The other end of the jumper wire goes down into a socket hole, with ANY Black wire.
The 24-pin ATX main power cable, is connected to the 24-pin ATX main power cable connector, on the motherboard.
Just as shown in the photo to the far right on the Playtool link.
The back of the 24-pin ATX main power cable's connector, is where the wires come in.
(The front of the power cable's connector is plugged into the motherboard)
I use a jumper wire that is approximately 3 inches long. (7.62cm)
An insulated wire. Both ends of the insulated wire are stripped of insulation, approximately 1/2 inch. (1.27cm)
One bare end of the jumper wire, goes down into the socket hole of the Green wire. Right next to the wire.
It has to go pretty far down in there.
At the end of each power wire, going into the 24-pin ATX main power cable connector, is a metal terminal pin. (Actually is a round hollow metal pin)
The jumper wire's bare end Must touch that metal pin.
The other end of the jumper wire, goes down into ANY socket hole with a Black wire.
(ALL Black wires are Ground wires)
Power Supply (Computer) plugged into power, the jumper wire is inserted.
The contact is a very BRIEF one. No more than 2 seconds.
(The Power On switch is a Momentary Contact Switch)
I suggest you also check the 12 Volt power rail. Check it with everything plugged in, inside the computer, and the computer on.
You need the Power Supply to have a load to get an accurate test.
There are 3 Voltage power rails in the Inspiron SMPS.
(Switched-Mode Power Supply, or just Power Supply for short)
A) The 3.3 Volt power rail
B) The 5 Volt power rail
C) The 12 Volt power rail.
The main one to check is the 12 Volt power rail.
[Orange wires are 3.3 Volt.
Red wires are 5 Volt.
Yellow wires are 12 Volt ]
The Positive (Red probe lead of the multimeter, is connected to any Yellow wire, coming out of the Power Supply.
The Negative (Black) probe lead of the multimeter, is connected to any Black (Ground) wire.
See if there is an unused standard 4-pin Peripheral power cable.
It has 1 Red wire, 1 Yellow wire, and two Black wires.
Connect to the Yellow wire, and to one of the Black wires.http://www.playtool.com/pages/psuconnectors/connectors.html#peripheral
[Multimeter function set to DC Volts. If it has it, set it to the 0 to 50 Volt scale]
11 to 13 Volts is Okay, but I prefer the voltage to closer to 12.
11 Volts indicates it's time for a new Power Supply.