Power Supply problem Bob.
Weak voltage power rail.
Allow me to explain what is going on;
1) Monitor is working OK. Shows No Signal.
Means No Video signal is getting to the monitor. This is because the computer isn't working.
Monitor goes to Sleep Mode, or Power Saver Mode, to conserve power.
2) Orange LED comes on, and fans spin.
Light Emitting Diode, so it is a LIGHT.
A) If ALL the LED's were on at once, they would use LESS than 1 Watt of power.
B) EACH fan uses 2 to 3 Watts of power.
C) A typical CPU (Processor) uses 51 to 125 Watts of power.
Hmmm, HP Pavilion M8400f Desktop PC?http://h10025.www1.hp.com/ewfrf/wc/product?product=3686665&lc=en&cc=us&dlc=en&lang=en&cc=ushttp://h10025.www1.hp.com/ewfrf/wc/document?docname=c01374051&tmp_task=prodinfoCategory&cc=us&dlc=en&lang=en&lc=en&product=3686665
(Showed you the path)
Hardware / Base Processor;
AMD Phenom-9500 (A) 2.2 GHz (95W)
Uses Up To 95 Watts of power.
This is why the simpy LED's light, and fans spin; BUT there is NOT enough power to turn the Processor (CPU) on.
Method to repair is up to you Bob, but I would recommend testing the 3 main voltages coming out of the Power Supply, with a multimeter; OR using a KNOWN to be good, Compatible power supply for a temporary test unit.
Or you can buy a replacement Power Supply.
I would just like you to test the Power Supply, or use a temporary replacement, so you do not rush out, and buy a Power Supply; and find this wasn't the problem.
A economical multimeter, (But is plenty good enough for this test), can be purchased for as little as $5 to $12.
An auto parts store is bit one example. (Although usually a little more pricey)
I have seen them on checkout aisle racks, at major discount stores.
The dangerous (100 to 240 Volts AC. Depends on what country you are in), voltages are KEPT within the metal case of the Power Supply.
The voltages coming out are 3.3 Volts, 5 Volts, and 12 Volts.
All are DC Voltage.
In comparison two D cell flashlight batteries produce 3 Volts DC.
Replacement Power Supply?
Try the easy method.
Type - Pavilion m8400f power supply in your search bar, and press the Enter key,
From one search hit,http://www.sparepartswarehouse.com/HP,Media-Center,m8400f,KJ377AA,Computer,Power-Supply.aspx
To the right of View Details states 5188-2625
That is the HP part number
Search HP 5188-2625,http://www.amazon.com/s?ie=UTF8&keywords=hp%205188-2625&page=1&rh=i%3Aaps%2Ck%3Ahp%205188-2625
This particular search hit has various examples shown.
ALL examples are ATX.
ATX is a Form Factor,http://en.wikipedia.org/wiki/Computer_form_factor
Originally designated for Motherboards. (Mainboard)
Went to Power Supply's, and computer cases, also.
An ATX form factor for a Power Supply, designates it's size, and shape; plus the types of power cables coming from it.
(Also the inherent technology)
Size and Shape:
Approximately 6 Inches Wide, 5.5 Inches Long, and 3-1/2 Inches in Height.
(152.39mm Wide x 139.7mm Long x 88.89mm in Height)
If you buy an ATX power supply nowadays, it will have the correct power cables you'll need, and probably ones you do not need, plus more than you need.
Works out pretty good, huh? Just wrap the power cables you do not need, with PLASTIC tie strips, and up out of the way.
(DON'T use bread ties. They have a metal strip in the middle)
The original Power Supply is reputed to put out a Maximum rated Wattage of 300 Watts.
A computer ONLY uses the power it needs, and NO MORE.
If you put a 10,000 Watt Power Supply in, and the computer only needs 100 Watts for what it is doing, it ONLY uses 100 Watts.
You should use a Power Supply, that is rated at least 10 percent more than what is needed.
One example of a replacement Power Supply,http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=3276575&CatId=1078
I can step by step guide you in testing the voltages, with a multimeter; and also in replacing your Power Supply.
Post back in a Comment.