If you download the Tinycore iso, or another file, you can check if it has been corrupted by verifying the md5sum.
To check the md5sum while running Tinycore or another Linux distribution, open the terminal and type:
cd path md5sum name
For example if you had the file tinycore-4.5.6.iso in /home/tc/dl, you would type:
cd /home/tc/dl md5sum tinycore-4.5.6.iso
Compare the md5sum generated, with the one on the site you downloaded Tinycore from.
In case of the example above, the output of the md5sum command should be:
For our example, the reference value to compare with, will be in file http://distro.ibiblio.org/tinycorelinux/4.x/x86/archive/4.5.6/TinyCore-4.5.6.iso.md5.txt
If the md5sum is different, the file has been corrupted during the download.
To fix things, delete the corrupted file and try to download again.