Are you aware about broadcast storms? Perhaps you somehow accidentally introduced a loop in the network? The symptoms fit that exactly. https://en.wikipedia.org/wiki/Broadcast_storm
STP is meant to prevent that. https://en.wikipedia.org/wiki/Spanning_Tree_Protocol
Of course you can't set up STP with unmanaged switches, so until you go managed and set up STP properly nothing will change.
It could be missing IGMP Snooping Protocol support in a network with IPTV or custom VLAN setups. There are 3 versions (IGMP snooping (v1, v2, and v3)), managed switches have them all, unmanaged usually don't have them. To avoid problems, only pass a single VLAN to the unmanaged switch (it must be behind the managed switch for that), otherwise the unmanaged switch can and usually will bring a network down after some time. Or just use a switch with IGMP snooping support.
I was not! Thanks for the hint!
Although I'm 100% sure there are no loops, I haven't changed the actual cable layout in ages.