I had a previous dropbox account and I deactivated it now all my files have disappeared of my computer. Does this mean they were deleted and are gone forever? Or is it something to do with my computer?
The account deactivation and files disappearing of your computer aren't related to each other in any way. If I have to bet, most probably you have had active "Dropbox backup" feature and, after account deactivation, you have deleted your Dropbox directory. Am I right? 🧐 If so, that's where your files have been getting away from in time of folder deletion. While "Dropbox backup" feature (you can think of as a bug) is active, all folders, object of backup, get move into Dropbox folder and stay there till the feature turn off. According you description you didn't turn the feature off, so the files (object of this discussion) were been still there and got removed together with the folder. Forgetting to turn "Backup" feature off before account deactivation is one error leading to the reported result. 🤷
... Does this mean they were deleted and are gone forever? Or is it something to do with my computer?
That depends on your Dropbox folder (and content) state at the last moment before you get your account deactivated. Have you used "Smart Sync" feature? If not, no problems in such direction. If yes, did you make sure all your folder content gats local in advance? If there is something in status online only, you have lost the particular thing forever. The files in sync locally at that moment (the moment of deactivation) has a chance for recovering. The last thing, you must not have done, is trash flush! If your trash is empty, everything got lost. If not, try to recover whatever you can.
You may need to restore your local account folder positions - Desktop, Download, etc. (in place where they were before "Backup" activation). That's it.