Yeah you will need to put it together yourself, but don't be too intimidated. I built my first complete desktop PC only a few years ago, before that I was comfortable swapping out components and I figured it was time to build one of my own (and it was the first time I had money for it.). I definitely watched a few videos on pros building a PC, newegg and linustechtips and ncix make pretty good videos of this, they go through the entire process and a lot of times point out a few mistakes people often make. Also
www.tomshardware.com forums are very great if you have any questions or you want to make sure some components are compatible with eachother, great source of knowledge there much better than I could ever offer you. They have a lot of guides related to building PC's as well. While I built my PC I had my smartphone logged onto google so I could watch the guides of people building a PC as I was building mine, It really made it pretty easy and definitely saved me time and the frustration of making more mistakes than necessary.
Expect to spend a good portion of a day putting it all together and installing windows and all the drivers and stuff. Sometimes it can be a little frustrating at times but after building my PC I found that I really enjoyed the process of building a desktop, Was a lot of fun fitting all the pieces together and making it have very tidy wire management and good airflow and cooling etc... and when you finish it and its runs great you get a great sense of accomplishment :3 or at least I did lol. You will save a good deal of money building a PC by yourself, You will most likely learn a lot about computer components and how they work together in a PC which is a good skill to have, and your finished desktop will feel like a custom project instead of a factory construction line prebuilt PC.
For your laptop, most likely the stuff you can salvage off of it aren't really ideal for a new desktop P build, I could be totally wrong here... ram and the hard drive would probably be the most likely components you could possibly use off of it. If it has like a 1tb Hybrid Hard Drive or maybe even a solid state hard drive I might consider taking that out and putting it in my desktop... Ram is relatively cheap these days and I'm not sure if the ram sticks used in laptops are the same size/fit as desktop ram?
First though I would try reformatting the laptop and seeing if a fresh install of windows on it fixes the problem. It's pretty easy to do if you have the windows CD and the key associated with it... if not it might still be possible off of a flash drive but again I'm probably not the best person to listen to when it comes to this, I suggest looking into reformatting your laptop on youtube and finding out exactly what you need and how to do it. If a reformat/clean install does fix the laptop, most likely the laptop will be worth a lot more keeping it together and functionable rather than parting it out for the small amount of money you would save trying to use the hard drive or laptop memory in a desktop build.
Also one more thing I will mention, I would recommend trying to get a GPU (graphics card) with 4gb of memory or more. I built my system with a GTX 770 2gb card and back then (a couple years ago) nobody was really saying I would need more than 2gb for games running in 1080 resolution on a single monitor, and it was true back then. But lately there have been a handful of PC games that are pushing past that limit and are a little more demanding when it comes to GPU memory. (assassin's creed: syndicate, just cause 3, probably Warhammer: Total War too.). Having a 2gb card is definitely my biggest bottleneck on my machine when it comes to most games I have had to turn down the graphics for... Right now everyone's starting to phase out 2gb graphics cards, so the price difference between a 2gb card and the same card with 4gb might seem like a big difference, but it's one area I would recommend forking out the extra cash to get the extra GPU memory.
Once again I'll list my most useful resources I've found while building and upgrading PC's
"Linustechtips" on youtube, Great for finding cheap PC builds and performance tests, also many videos which explain components how they work and computer processes quickly without putting you to sleep... Definitely worth a subscribe. Also he does a lot of PC Build experiments... such as building a giant plumping network through his house to act as water cooling for a bunch of PC's or trying to build a PC inside of a minifridge for cooling and testing the results
"NCIX Tech Tips" on youtube, A handful of PC hardware, components, and peripheral reviewers including Linus from the above youtube channel. Very good for finding reviews on specific hardware components, They are probably my most trusted source on finding out if a component is worth buying or if I should pay extra for something else. Or simply just seeing the performance difference between 2 different graphics cards for example. If something isn't worth buying or the performance upgrade just isn't there for the price jump involved they will tell it to you straight.
Newegg.com Goto place for finding average prices on computer components as well as some videos of PC build guides, overviews of computer hardware components and their features... But mostly I use newegg to check for prices (not always the cheapest, but usually if they aren't the cheapest they are only a very small amount above the cheapest retailer. They have great prices overall.)
tomshardware.com best place for tech forums, if you got a specific question regarding PC tech most likely someone has asked that very same question already on their forums and also most likely that it has been answered already. If not you can ask it yourself on the forums and you will usually get some pretty good responses/answers within a matter of hours.
Have fun buying and building a new PC