more likely than not you are having a hardware issue with your ram, power supply, HDD, or motherboard. If it was a software issue then you would typically get a boot loop where it randomly reboots during startup, or the system would simply hang. Blue screens, and grey screens are hardware related, so I would go that route first and see if you can diagnose things that way.
Most pre-manufactured computers have a restore partition on the HDD that you can access via a shortcut key (like F10 or F12) which will walk you though the restoration process. However, if the HDD itself is the issue (which is a common problem as HDDs have moving parts and are typically the first thing to die in a computer), then you would simply be up a creek. When you purchased your Dell you had the choice to purchase backup DVDs for $20, which you can boot from and use to bring the computer back to factory spec, and when you first turned on your computer you should have been prompted by Windows Vista or 7 to make backup discs for this very reason... but nobody does this.
If the drive is dead (not saying yours is, but it is a possibility), and you do not have restore discs, you can order them from Dell, but they typically start at $40 for current models, and get more expensive the older the computer is. After ~5 years they will no longer have a copy, and then you need to purchase a new computer, or else buy yourself your own disc copy of Windows to replace it with. The other option right now is that Windows 8 just came out and is only $40 for the disc copy at places like Microcenter and Staples, which would get you the latest version, as well as be generally cheaper than other options available. The only trick is that you have to learn win8, which is quite different from previous versions. Not bad... but there is a learning curve to get use to.
To test your system you will want to try a few things to start with:
1) memtestx86+ is a free program that you can burn to a CD, boot from the CD and let it do it's thing for ~2 hours per GB of ram that you have to be sure that things are OK.
2) find a Windows disc, and under the repair options there will be some diagnostic tools such as Disk Check (which will check HDD integrity), and Windows Memory Diagnostic.
3) if the computer passes those gauntlets but still having hardware issues then it is time to break out something like PC Check which will test many aspects of your computer for issues.
4) do a visual inspection to check for anything that looks charred, dirty, or capacitors with blown tops. Even the smallest visual flaw can make a system not work properly.
5) reset your BIOS settings to the default. Sometime BIOS gets confused, and causes issues, and simply needs to get set back to normal for things to work properly.