1) A bad power supply ($50-$75 generally) could make your system do all kinds of wacked out things. It might cause it to crash unexpectedly, never truly start up, or it might even get most of the way into windows and then suddenly freeze. I generally suspect the power supply when someone tells me about a multitude of problems (like your system is doing all those things you mentioned and not just one of them) as it will cause different things to happen at different times.
2) Failing hard drives ($50-$75)could show itself as corrupt data, the system wanting to boot into safe mode, random system freezes, or even the Blue Screen of Death (BSOD). Now while all of these sound similar to the problems of a failing power supply the differences are there, but unfortunately unless you are a computer tech, you might not pick up on them. There are diagnostic tools you can run against your hard drive, but that would be a discussion for another day.
3) The RAM (memory) in your system has "gone bad" (about $100). While this is a less likely scenario it can happen and will again cause all sorts of different responses. As with the hard drives there are diagnostic tools to use to test your system memory.
4) Video card isn't working ($60). This is one of the easier items to detect as you will SEE what it is doing. When a video card fails it generally is fairly evident as your display will no longer show anything, or the text becomes all garbled.
5) Motherboard or CPU is beginning to fail ($200+). This one would most likely be a definite death sentence unless the system was less than a year or so old. However, this could be one of the toughest items for the casual user to determine as bad so it isn't too easy to make this call.
6) No bad hardware, just a tired old operating system (Free - maybe). Windows is a bit of a fickle operating system and over time it tends to deteriorate just from normal use. Installing and removing programs leaves traces of old software that can build up to quite a nasty mess. If you are diligent about backing up your data (you ARE right?!?!) then you could put in the disk that came with your computer and "wipe" it clean. If you have a name brand system (Dell, Compaq, Gateway, etc) then most of those have disks (you may have had to burn them yourself) that will restore the system to exactly the way it was when you first brought it home. BEWARE though that these disks do NOTHING to save your data, if you put the disk in and just run it without making sure you have everything copied off your system that you need, then you WILL lose your data.
The bottom line is what do you want from your computer. Were you wishing (when it was still working "OK") that it was a little faster, or that it had this or that feature? If so then you probably want to look at something new. If it was handling all the tasks you wanted from it then maybe getting it repaired is a better alternative. Just as there are many possibilities to why your computer is doing something wrong, there are multiple factors into deciding to just replace the whole thing.
Hope that gives you a little guidance in making a decision. Just remember that somewhere around 70% (that number is made up by me, but if anything I would expect it to be low) of the computers out there are NOT utilized to their full potential and most 5 year old computers are still way more than capable of doing what most people need from them. Just like with a car, they need a little maintenance from time to time as they won't run indefinitely when ignored. Doing some routing servicing could get you several more years out of what you already have.