A forensic analysis of the pilot's notebooks will provide the truth, will be very simple, if they were asleep then there will be no HD writes during the 80 minutes.
Unfortunately, it isn't quite that simple. Modern PCs have a great deal going on inside of them even when they are "idle," so it's very difficult to tell what has been done with the PC over a specific, short period of time. No record of mouse activity, keyboard input, or disk activity is kept beyond the simplest statistics, and the disk drive is regularly used for both reads and writes even on a completely idle system.
A keylogger or other special software could provide a useful trail (grossly similar to a CVR or FDR), but such gadgets are not normally installed on ordinary PCs.
You can get an idea of what a PC is often used for, or has been used for in the past, by looking at what is on the disk drive(s), but you can't really reconstruct specific activities in the past. You could establish that a porn site had been visited from the PC, for example, but you wouldn't necessarily be able to establish what had been done on the site. Figuring out if and how pilots used their laptops during a specific 78-minute period on a flight would require finer resolution than an examination of the disk drive is likely to provide.