Lost the screws that attached to the TV stand for KDL-40S4100. What type are they and where can I get replacement?

If you wish to get some details; check the site linked here. Pull up older posts.
http://electronicshelponline.blogspot.com/
Troubleshooting procedure for No-Picture is given in detail.

very easy there are just a few screws that hold the board to the chassis and then its a simple unplug the old boards wires then install the new board and replug the wires.

Main PCB is bad . I just got the information from a Sony authorize servicer price for the part only $504.87

There are 4 screws in Sony KDL-26S2010 that connect stand neck with tv and part number of screws is 258060201 .. SCREW, +PSW M4X12 available in partstore.com for $1.25 each

Look for one on EBay under Electronics TV/Parts
Mats Electronis 1-800-628-1118
MCM Parts 1-800-543-4330

The only solution to this problem would be to contact Sony directly and order a stand.

TVs are sold in the box with one single stand and the electronics stores don't receive extra stands to sell to customers. Ordering a stand from the manufacturer generally costs less than $100.

is there sound come or your tv goes in stand by mode or not.if not then try to use other inputs. maybe there is problem with only one input.
is there back light on?if yes and sound come on all in put then you have to update softwear from sony site.

Probable power supply

There is a problem with the processor. The only way to resolve this issue is to replace the main board. It is called the A board in your TV.

There are two for this model and the correct one will depend on what your serial number is.

Part numbers are as follows:
part # 185709211 for Serial #
1,000,001 - 1,350,000
1,700,001 - 1,750,000
1,800,001 - 1,804,270
1,804,271 - 1,818,372
1,818,373 - 1,830,000
list price: $504.87 core charge: $680.00

part # 185709231 for all other serial numbers
list price: $505.87 core charge: $600.00

I might have one of this table top stand.
Write to [email protected] for more info.