I have LR 5 and Elements 10. I think both are a 2 time download. My hard drive on my PC just crashed and had to replace it. Now my computer over heated itself and I will have to by a whole new tower. My question, will I have to go buy these programs ALL over again or is there some way around it where I won't have to re purchase both again?
You can download Lightroom an infinite number of times.
You can use your serial number to register Lightroom on two machines, as long as you are not using Lightroom simultaneously on both computers, and both computers are used for your own personal use. If a computer/hard disk crashes and can't be used, that doesn't count as one of your two installations.
So really, nothing is stopping you from using Lightroom and you don't have to purchase it again.