Terje, what you're really asking is whether the Linux KERNEL can handle a drive that size--it doesn't matter whether it's Slackware, Arch, Fedora, or Ubuntu, they all run the (mostly same) Linux kernel. As Wigry's link to the Wikipedia entry shows, for newer file systems, ABSOLUTELY! Since this isn't a server we're talking about, you are extremely unlikely to ever come close to any of those limits.
I also have a suggestion: if money and capacity aren't too big of issues on that machine, replace your failed HD with a SSD instead--the speed-up you will see will blow you away! I dropped an SSD on my 4 year old laptop and it was almost like buying a new machine...well, except for the graphics, of course!