I would suggest this generic Power On switch,
and the Red, and Black twisted pair of wires go to the Power On switch.
Your statement of ,"....don't know which of the colored pairs of wires go.....", leads me to believe you may have all of the Front Panel wires disconnected.
How about information as to where ALL the Front Panel wires go?
(Provided I have correctly interpreted your statement)
Back in the time that the eMachines T2542 was made, TriGem was the motherboard manufacturer.
The Model Name of the motherboard is Imperial, and the Model Number of the motherboard, could have been one of four variations offered.
Model Name: Imperial
Model numbers could be G, GL, GV, or GLVE
(Imperial G, Imperial GL, Imperial GV, or Imperial GLVE)
ALL four variations used the same Front Panel header.
(The connector on the motherboard the Front Panel wires connect to, is named the Front Panel header)
I would like you to view this page,http://www.e4allupgraders.info/dir1/ecase/support/front_panel_header_support.shtml
Scroll down to the heading -
Trigem Imperial Front Panel Header Pinout.
A) Pins 1, 2, and 3 are for the Power On LED light.
B) Pins 5 and 6 are for the HarDDrive activity LED light.
(Pin 4 is not used. NC. No Connection)
C) Pins 7 and 8 are for the Power On switch
D) I wouldn't connect any wires to Pins 9 and 10, nor Pins 11 and 12
E) Pins 14 and 15 are for the Reset switch. (The button you press to restart your computer.
If the T2542 doesn't have a Reset switch, don't worry about it. There are many other ways to restart your computer)
F) Pins 17 18, and 20 are for an internal speaker.
This speaker is used for BIOS Beep Codes.
In the chart to the right, you will see GRD used many times.
GRD stands for Ground.
ANY Black wire in the twisted pair of wires, is a Ground wire.
Most of the eMachines I have worked on, use a Red, and Black pair of twisted wires for the Power On switch.
I could be mistaken on the T2542.
Best method, is to follow the color code of the wires that come from Pins 7 and 8, and be sure.