You could buy an external drive case, remove the hard drive from the old computer and put it in the external case. Would need more info about your old computer in order to advise what case you needed and such. You'll want a case with it's own power supply. Post back with the make and model of your old computer.
What type of tablet do you have? Is it an iPad, Android or Windows tablet? Post the make and model of the tablet so we can advise on how you could transfer and use some of the files such as documents, pictures or videos on your tablet. There really isn't any limitation on "data" files other than your tablet probably won't have enough storage space to accommodate all of your files at one time. You could leave them on the external and access them from the tablet. The tablet having a touch interface does not represent a limitation in anyway as to which data files you can access. Programs won't be able to be transferred. If the old computer was running Windows and the tablet is running Windows, you could re-install your programs on the tablet but, as a general rule, programs cannot be transferred from one computer to another.