BIOS Post
Ok, no worries. BIOS Post means "Power On Self Test". This is the stage where the bios identifies the physical components attached to the motherboard and determines how they will communicate with each other.
I have a feeling that your bios is not posting, meaning that your motherboard does not recognize all the physical components attached to it.
Graphics
That processor has graphics. If the motherboard has onboard graphics, seen by the video connections on the rear panel, then it would be best for now to test the setup with the onboard graphics. You can add your video card later after you know everything else is working well.
Hard Drive
Connect a hard drive to the motherboard. I forget right now if one is specifically necessary for the bios to post but I think it might be.
Heatsink
Or, there may possibly be problems with the cpu heatsink and thermal paste causing an overtemp situation but I do not think so. I expect you do not need to remove your heatsink again. By the third time, you are near certain to have positioned it correctly through practice.
Thermal paste squeezing out the sides is acceptable. It shows too much paste was used but the compression holding the heatsink against the CPU squeezes out the excess. Sure, maybe the thermal paste layer is too thick but it can be accepted. You did well with cleaning. The main purpose of the alcohol is to remove any grease or oil from your fingers. When reapplying like this, the cpu and heatsink do not need to be perfectly cleaned with alcohol since the thermal paste remains good but it helps to remove as much as possible before a fresh application.
Applying Thermal Paste
You will see in the image below numerous examples of thermal paste applications. I added brief notes where useful so you can get an idea.
Here is a website that provides a good method with quick explanation.
Best way to apply thermal grease to CPU correctly
Google -
how to apply thermal paste to cpu
It can be difficult putting your first build together on your own. You are doing well. Hang in there, think each step through carefully, and ask when help is needed.
Make sure to keep yourself grounded to prevent any static electricity from potentially damaging components. I like to make sure that I touch the case to discharge any built up energy before touching any electric components. Then I like to keep my forearm pressed against the case to stay grounded. Be careful on carpet with socks or slippers, but this is mostly an issue in the cold, dry winter months.
EDIT:
Can you provide your motherboard; make and model?