If staff are too "snowed under" to help their tuttees then perhaps they should reconsider their workloads. Staff are PAID to support students, they aren't volunteers!
Wow cat, do you realise how petulant and entitled that sounds? More to the point, it suggests you understand very little about what being a lecturer involves, even though you're complaining about one.
To start with, academic staff don't set their own workloads. We are usually given a workload allocation by the head of dept or similar, and teaching (that's all forms of student contact, not just stand-up lecturing) typically takes up a minority of our workload - for instance, in my dept, 20-40% of a staff member's time is meant to be spent on teaching, with the remainder spent on research and admin/service. As such, it's not possible for us to "reconsider" our workloads when we are overburdened. I wish it were. As it is, most of us work far, far beyond our contracted 37.5 hrs/week just to keep head above water.
A supervisor taking 8 days to respond to an email during teaching term wouldn't be acceptable in my dept (ok if it's outside teaching term as people are at conferences and on hols), but we also accept that it happens to everyone occasionally. When you're getting up to 100 emails a day, it's easy to miss one when you're overworked, or when you're ploughing through a backlog of email because you've been off sick for a few days, and so on. For these reasons, we expect students in such a situation to be more proactive about making contact if they don't get a response to an email when expected. We expect them to send at least one follow-up email, go in person to the supervisor's office, ask in the undergraduate office if the supervisor is actually around or ill / away / etc. Only if multiple efforts of proactive chasing failed to make contact, or if 8-day delays were a regular occurrence, would a supervisor be considered unreachable and therefore not providing students with adequate support.
As it is, as pp noted, there's not much substance to your complaint on the basis of the info provided. You still sound quite angry about the situation, however, even though it seems to have happened over a year ago and was resolved when you switched supervisors. Are you still angry?