If you think you have a virus, then you need to run your anti-virus program. If you don't have one, you can download AVG for free. I would also dump all the programs you don't use but can download later if you need them, to free up space. I would also dump your cookies and history, and then download and run a program called AdAware.
Whether or not you have a virus can only be determined by running a reputable virus scan program. Some are available for free online such as Avast, AVG and Panda. You may have to download the software to a flash (or thumb) drive if your hard drive is not allowing downloads.
Just because your computer will not allow you to download anything doesnt necessarily mean you have a virus .You may have to go back to your computers setting and see how its set up, some computers will not let you do certain things until you go and specify your preferences.
You could very well have a virus and if you do you can run an anti virus scan called AVG or Avast to see if there is anything there or not. Sometimes they will catch a virus and be able to remove it but sometimes they can't remove it and you will need to have your computer wiped clean. You may have a firewall blocking you from downloading anything and if that is the case you just need to go in and remove or turn off the firewall.
You haven't supplied enough info to answer...can you access internet? You can find some free virus scans online (Symantec/Norton has one) and that will at least tell you if you are infected.Also the other ans are valid. However there are often other solutions before having to format the hard drive (erase it) and then put back an operating system (eg Win XP...), and all the programs you want from the to be wiped machine (which can be a problem if you don't have original CDs or a set up program to install it), and then of course there are all the files you may have created. It is by the way always a good idea to have an external hard drive to keep backups on. Hope that helps...if you explain your computer skill level it would help people to answer.