Bad Power On switch, or bad Power Supply.
(Weak voltage power rail)
The Power On switch is located inside the plastic Power On button.
This is an example of a generic ATX power on switch,http://www.directron.com/atxswitch.html
One that I have found fits many desktop computers.
There is a test to see if the problem is the Power On switch, or the Power Supply.
The test requires using a jumper wire on the ATX main power cable's connector.
Jump the Soft Power On wire (PS_ON) to ANY ground wire.
This is Lenovo Support, ThinkCentre S51 desktop computer, User Manuals, and the link to download the HMM.
Hardware Maintenance Manual.
Left-click on the top blue file listed.
Starts with - Hardware Maintenance Manual (HMM) (March 2009) Thinkcenter A51........and ends with S51 (type 8098, 8171, 8172, 8173)
Date to the right is 2009-08-05
On the next page look under the heading - File link, and click on -
19r0486.pdf in blue.
This is a PDF file. It may take as much as 30 seconds before you see the first page. Additional time may be required to fully download. Let the file download all the way before looking through it.
(Took 4 seconds to see the first page, and over 3 minutes to fully download just now. Medium speed DSL connection)
With this HMM you can follow along with illustrations, and details, as I detail how to perform the above test, on your IBM ThinkCentre.
(FRU = Field Replacement Unit)
S51 is the Product Model.
There are several Types.
Page 98 details how to open the ThinkCentre S51 desktop computer. ('Pizza-box' computer case)
(Types 8095, 8141, 8142, 8145, 8420, 8421)
Page 123 details how to open the ThinkCenter desktop Tower computer case.
(Types 8143, 8144, 8146, 8422, 8423, 8427)
Page 145 details how to open another 'Pizza-box' style computer case.
(Types 8098, 8171, 8172, 8173, 8424, 8425)
Computer unplugged from power, observe Anti-Static Precautions, BEFORE you reach inside.
Your body carries Static electricity.
Static will fry out (Short Circuit) the hardware components inside a computer.
Computer unplugged from power, TOUCH the metal frame of the open computer case. Touch an unpainted surface.
This action will relieve your body of Static.
Should you leave your computer in the middle of working on it, be SURE to Touch the metal frame again upon your return.
With the flat desktop models, ('Pizza-box') you may have to release the lock, and tilt the Harddrive, and optical drive up. (CD/DVD drive)
This will allow viewing the motherboard.
With the desktop tower model you may have to ease a few cables over to view the motherboard.
You are looking for the 20, or 24-pin ATX main power cable.
(Don't know if your model uses a 20-pin, or a 24-pin.
This is what you're looking for,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
Scroll down to see the 24-pin ATX main power cable.
Look at the photo to the far right.
The Green wire is the Soft Power On wire.
ANY Black wire is a Ground wire.
With the ATX power cable plugged into the motherboard, as shown in the photo to the far right, you are going to insert a jumper wire down into the socket holes.
The jumper wire goes down in the socket hole, Right next to the wire that is in the hole.
It goes down in far enough to touch a metal terminal, that is at the end of the wire.
(Approximately 1/2 inch)
The jumper wire of choice is a paper clip straightened out, then bent into a U-shape.
The middle of the U is wrapped a few times with black plastic electrical tape.
(Trivia: One wrap of black plastic electrical tape is enough for 600 Volts DC)
The voltage you will be dealing with is 5 Volts DC.
Two D cell flashlight batteries produce 3 Volts DC.
You may wish to wear a glove on the hand that holds the jumper wire. There may be a small spark.
The Power Supply, (Computer), is plugged into power.
One end of the U-shaped jumper wire, is inserted down into the socket hole with a Green wire. (Right next to the wire)
The other end is inserted down into a socket hole with ANY Black wire.
The contact made is no more than 2 seconds. (1001, 1002)
If the computer comes on, (Power Supply actually), the Power On switch is bad.
If the computer does not come on (Power Supply), the Power Supply is bad.
It's an ATX power supply, probably a generic model made by Bestec, HiPro, Delta, or another low quality power supply manufacturer.
The Wattage is probably stated at Maximum 225 watts.
An ATX style Power Supply is used by over 80 percent of desktop computers out there. You can buy a decent one for around $30 US.
(Power Supply case size is approximately 6 inches Wide, 5.5 inches Long, and 3-1/2 inches Tall)
You can use a 300, or 400, or 500 Watt power supply.
Doesn't matter. Won't hurt the computer.
A computer ONLY uses the power it needs, and no more
Post questions in a Comment.