Ok, Since you are not a geek (per sey), then I assume that you didn't build your computer but bought it from a branded manufacturer. To solve the issue of replacing the lost disc...call the manufacturer for a replacement copy.
Now as for the other proprietary software that you have lost the discs to, you could possibly do the same thing there. Or you can get a good quality copy from a friend and use it with YOUR activation codes, as these are the codes that say it is legit or not. If you have a program on your system already then you can use this utillity and it will find what the codes are and you can make new hard copies of them.... perfectly legal as they have already been installed.
On the backup issues, most backup programs will only make back ups of your personal files and not any program files. There are some that will do backup every thing( called snapshots) and they are stored on either a seperate partition or burned to disc., to be reinstalled at a later time as needed. There are also programs that do ISO imaging this is like a layered photograph that is stacked upon itself a million times in which you only see the top picture.
When it is used it is slowly dismantled so as to replace all programs and files that were on your system at the time the ISO shot was taken..You will need to google as it is a little more complicated than that and not enough space to cover it.
Then there are regular backup programs that will back up everything and reburn it in a compressed state to a either a cd, dvd, or partition. You need to study all these to see which one is suitable for your needs.
Transfering information from one harddisk to another is also done in various ways. Some will only transfer your pictures and files and others will transfer everything from one disk to another.
Most harddisk manufacturers supply a utillity disc with a new harddrive or makes one to be downloaded from their home sites. These utillities have programs that will actually transfer eveyyhing from one disk to another...the key is that you must use the program supplied with the disk that you are transfering to.
Hope that helps.