I think it?s important to distinguish between signs that a computer needs to be replaced and signs that the computer is in need of repair. And when considering repair, we should distinguish between hardware repair and software repair (e.g. repairing or perhaps, ultimately, reinstalling the operating system (Windows)). Clearly a computer exhibiting any of the symptoms that you describe ... much less all of them ... is in need of some serious attention, but not necessarily replacement.
Pretty much anything that goes wrong with a computer can be fixed; it can ALWAYS be made "as good as it was when it was new". Almost all of the symptoms that you listed could be caused by either hardware failures or a corrupted operating system. If you brought the computer to me, the first thing I?d want to know is what is the vintage of the system and what components does it have, because assuming that I?m not working for free out of friendship, if you bring me a Pentium II or Pentium III system (or anything earlier, or anything that originally came with an operating system earlier than Windows XP), I?m probably going to tell you right up front that while I can fix it, indeed while I can make it ?as good as it was when it was new?, and while the cost may not even be all that high (say $75 to $150), it?s not worth putting even that money into what is now in computer terms a really vintage system. In fact, I?d probably give you that advice even for a very early Pentium 4 system (say made between 2000 and about 2002, with a clock speed under 2GHz). I?d only suggest putting repair efforts into something more recent than about a 2002 vintage Pentium 4 with a clock speed over about 2GHz.
Assuming that you are still game for a repair, I?d run a good memory diagnostic [Memtest or Memtest86] first, because bad memory can cause a multitude of problem, including all of the problems that you describe, and it?s relatively easy and inexpensive to diagnose and fix.
Once we got past that point, and in the absence of signs of other obvious hardware failure, I?d be inclined to reinstall the operating system (Windows), because even if a corrupted operating system hadn?t been the initial problem, if you are seeing this type and variety of problems, it?s an odds-on certainty that the copy of Windows currently on the hard drive has become corrupted and needs reinstallation. A corrupted operating system can cause all of these problems, but it can be either the cause or just an effect, in which case the actual cause could be hardware failure of any kind as well as virus?, malware (?adware?) and so on.
The act of completely reinstalling an operating system is actually a fairly good stress test for a PC, and by the time a complete reinstallation of the operating system is done (including installing your other software and fully updating everything), a good technician will have a very good feel for whether or not the system is ?stable? or needs additional diagnostic work to find additional hardware problems. [After memory, the most likely cause of hardware problems in an older PC is often the power supply.]
If the computer is not so old as to be inherently incapable of meeting your needs, the only real indication that it actually needs to be replaced as opposed to fixed would be a failing motherboard, which, in a sense, ?is? the computer. Short of that (and even motherboards can be replaced), nearly everything can be repaired, and the computer could be made as good as it was when it was new.
Very often, however, the only thing a computer needs to be ?as good as it was when it was new? is a reinstallation of Windows, followed by installation of your applications software and transfer of your data. While this is ?just software?, it?s time consuming (hours to as much as several days, depending on how much software, data and settings are involved and need to be transferred), and if you are paying for it to be done, there will be a real cost for labor, if not for actual parts. On the other hand, if you buy a brand new computer, it won?t have your software, settings or data on it either, and you may still be looking at a significant effort to get it to a point where it is loaded with your software and data and connecting to your internet provider and E-Mail. So even total replacement of your old computer with a new computer doesn?t immediately end or cap your computer issues. You still need to get your software, data and settings transferred and applied to the new computer.
I hope that this is helpful,