(1) make a FAT32 partition in your new computer
(2) copy everything from your old disk to this old partition. The reason you cannot access your files in old HDD is that HDD is in NTFS format which has security, once copy to FAT32 partition, all file securities are lost
if (2) does not work, you can try to use a imaging or clone program (e.g. True Image) to clone old HDD to your new FAT32 partition.