Observing (even a couple of) users or having them walk you through their tasks is really valuable. You seem to be aware of it but it cannot be stressed enough. You wrote that “interviewing the user is hard” but what does hard mean in this context? It still might be worthwhile to push for some access. You will need to talk to real users for the usability tests anyway.
You could also talk to the people managing the intranet in the IT department, enquiring about complaints or requests for help they might have received (if users ask for help about finding a particular info, it means that this info is useful to someone and that it's not easily findable). People putting content on the Intranet might also have something relevant to say (HR, etc.). What info are they still asked about which they would prefer people to look up online? Besides, they are users too, so they might have some issues of their own to report.
Also, without any sophisticated analytics package, some basic statistics (which page is the most visited or that kind of things) or log file analysis might be available or worth collecting, even if only for a few days. However, even if you had very good analytics, this cannot be the only source of data. It's perfectly possible that some part of the site is not visited at all because everybody knows it's not working well and prefers to fulfill this particular task in another way (e.g. phoning or sending an email directly to the responsible person).
If you go for a survey, consider asking focused questions like “What function do you use on a regular basis?” or “When was the last time you turned to the intranet and could not find what you were looking for?” rather than broad why and what-motivates-you questions. When planning the recruitment and sample size, keep in mind that intranet are even more likely than e-commerce website to have starkly different user groups.
Another technical issue to consider: The number of people you need for your survey will depend on your objectives (identifying a list of tasks/issues requires a smaller number of respondents than prioritizing these tasks or quantifying their importance) but whatever you do with the data, keep in mind that the error margin is much lower for a subgroup than for the whole sample. To take just one example, if 10 people out of 100 tell you that task A is the most important, you can expect that between about 5 and 20% of all users actually think so. But if, out of these 100 respondents, only 20 of them match a particular user profile (say they work in a particular country or a specific department or are managers, etc.) and 2 of them mention task A, your best guess would be that between 3 and 30% of that subgroup really consider task A to be the most important. Your uncertainty about that particular figure is much higher for the small subgroup than it is for the whole population because you are in effect trying to reach conclusion from a much smaller sample.
Finally, why does your client wants “the users” to define which tasks are important? Are they possibly trying to respond to some complaints from the workforce (and if yes, which ones)? There are all sorts of information that can only be obtained from the end users (as opposed to management or IT) but which tasks are relevant for the business is not necessarily one of them. Surely, the client invested time and money in this intranet for some reason. This could give you a cue to the relative importance of different tasks.