truescot

I just edited my answer and want to make sure you got what i said, IF its a case of you having limited cash and having to choose between a better processor, more ram, better gpu etc and an aftermarket cooler, then don't choose the cooler, you can always do that later as well and you will get the most benefit from the other choices

its a pain, but tbh not a big one, my suggestion would be to get an external HDD, copy off all of the information that you want to keep then re-install windows from scratch (you will get the option to delete partitions and format the ssd's at the start of the windows installation, definately do that).

that is really weird and fucked up, is there any chance you are getting condensation on the board?, low temperature should not be a reason for a computer not starting up, hell people are practically pouring liquid nitrogen on them(i am oversimplifying that a little), my guess would be something bizzare going on with the psu or a dodgy wire somewhere which shrinks when cold and expands and makes contact in the heat, but that is a real stretch as well tbh

it is totally possible it's the pump, i had a similar noise when the pump on my old h80i was on it's way out, very unlikely to be the motherboard, could be a fan in the psu(if it has one) as it also sounds like a fan with a broken bearing

check in the bios if it is set to uefi or legacy boot, change it to the other setting (most likely its set as uefi and you need legacy)

cloning is one way to go, if you have got new hard drives in the new machine, as viper9 mentioned Acromis is good for that (also check out hirens bootcd it has loads of nice utilities)  that being said, whilst you can transplant windows from one set of hardware to another I personally don't like it, there is always little problems that would bug the crap out of me and i never feel it is very reliable especially when you start looking at event viewer and getting paranoid.  If i where in your position i would consider looking at virtualisation and using p2v to transfer from the old server, it really does work well and virtualisation gives you a ton of options like adding a new vm when you want to upgrade windows for instance and transferring things over bit by bit till you are ready to go live with the new server.  Also means that if the server fails you can get any old piece of hardware, install the hypervisor and be up and running in no time at all.  ESXI is free for 99% of peoples use cases and i would always suggest going that route.

what can i say i have got 2 gaming laptops and a couple of gaming pc's (plus other irrelevent stuff) and frankly i never use the laptops for anything other than browsing the web, development, office etc and use the pc's for the gaming, keep the PC you will be able to use it a lot longer than the laptop, will be able to upgrade it, and even 10 years from now still be able to play games on it, the laptop will be 5 years tops and even brand new it wont be as good as the PC for gaming, so long story short keep the pc and get a cheap laptop

what can i say i have got 2 gaming laptops and a couple of gaming pc's (plus other irrelevent stuff) and frankly i never use the laptops for anything other than browsing the web, development, office etc and use the pc's for the gaming, keep the PC you will be able to use it a lot longer than the laptop, will be able to upgrade it, and even 10 years from now still be able to play games on it, the laptop will be 5 years tops and even brand new it wont be as good as the PC for gaming, so long story short keep the pc and get a cheap laptop

Being that it all works when the platter drives are unplugged it is almost definately one of those that are the problem.  It is not uncommon for a computer to freeze like you are mentioning when one of the platter drives that has been parked decides to spin up, it is not normally noticed on a system that is using the platter drive all the time as it does not go to sleep but as you have got 2 ssd's most likely doing the lion's share of the data access the hdd's go to sleep and sometimes wake up just because windows chose that moment to poll them.  There are 2 ways to approach this, the first is to get rid of platter hard drives completely out of that system and just keep your big stuff on a nas or something else externally, the second way is to stop your hard drives going to sleep, you can do this in the windows power options and changing the plan so that the hard drive never goes to sleep.

exactly the same comments as sansvarnic, except if you don't have another pc at hand try getting a cheap hard drive caddy with external power

yea, malwarebytes is fine as long as you got it from a good location, also check what is running under task scheduler and what starts with the windows

And, if that not fixed it, with the information you shared: buy a new Computer. (@Moderators why isn't there a template when you open a new topic in Troubleshooting like in the New Builds section?).
 
Edit: this might help: 
 

it is 100% safe, if you do not have the operating system or program files on that disk anyway there is nothing that can go wrong.  It is an operation i have carried out litterally 10's of thousands of times in my 25 years in IT operations , or if by safe you mean that anyone who has got your hard drive has access to your files, then yea, the only way around that is to encrypt your drive 😛