I have a 1995 Silverado-1500 series and the problem that I have is that power doesn't reach the glow-plugs...

You first need to unhook the shift cable from the top of the gear box , then carefully remove it from the gear liver linkage and follow the reverse step to fix the new one. I am sharing a video of GM hope it will give some refrence .

Remove the button & resolve that part of the issue,
so it either works or if tests bad-- replace it

With most relays, you have 4 wires. One is power to the component the relay controls, one is a ground to the relay magnet, one is power to the magnet, and the fourth goes to the component, in this case the glow plugs. The ground usually comes from the computer.
With the key on you should have power to two terminals and you would jumper the hot terminal to the glow plug terminal. Or use a test light or meter to check for power on the glow plug circuit.

Replace your plug wires and make sure you have each of them connected to the correct cylinder. Check the Earthing (grounding) of the starter and battery circuits. If this doesn't solve your problem then there could be a problem with your alternator. Clean all the terminals on your starter and alternator and give it shot. There is a specific CRC brand spray for cleaning electrical components... do not use WD-40 or it can ruin them and ruin the accessory belt too. Remember, plug wires are only good for 60K miles or so, don't expect them to last forever. While you are at it.. check your spark plugs... a broken plug can play havoc with diagnostics... do not overtighten. I recommend Denso Iridium plugs for gasoline powered vehicles and Denso Glow Plugs for diesels... they last a bit longer than the OEM Bosch glow plugs.

remove grill ck horns with jumper wires ck plug for power, if horns work .if horns dont work with jumpers replace . if no power ck fuse if good relay for signal and power if no signal when horn pushed either horn switch in airbag ,or cable reel witch need cked with special srs tools .

Sounds like it might be a cv joint or also called the cv halfshaft.

How did you inspect your parts. Sometimes a part might look ok when actually it is bad. When was the last time you replaced your Fuel filter? I would perform a fuel pressure test. You may have a weak fuel pump. You don't list checking your plug wires. You may have some bad plug wires. Also remove your rotor and look in the distributor. There is a part located under where the rotor goes that is a ceramic type of material. I can't remember what they call it but inspect it for cracking. Is is a fairly common thing. If you see cracking you will need to replace the distrubutor shaft which is not a big deal or you can buy a remanned distributor if you don't want to mess with it. Also you may have an EGR valve that is sticking open which could cause your symptoms.

check if there is a spark, and if they are wet, (if gasoline), if diesel, check if the glow plugs have diesel on them, and that they are glowing when power is applied

glow plug controller.it is located on the right rear of the engine and looks like an old ford starter solenoid.It has a big power wire going to it and a couple of little wires. They are your signal from the ignition switch and the other is for your glow plug light. Replace the controller--not too complicated-just mark which wires go to what and its pretty simple.

Glow plug relay or the glow plugs are not working the way they should. Also check the cold start solenoid.