The first case would appear to be the router failing because of poor manufacture or components, this is hardly a surprise - Speedtouch modems are crap.
The second case looks like something a little stranger, but again I think it's the router. I've never heard of the brand and I don't trust network gear from people I've never heard of.
My suggestion is try buying a decent router, like a NetGear or Linksys. More money, but they are decent boxes and won't feck you about. If that doesn't work then you have a more serious problem. Buy a new cable to link to router up too while you are at it. If you have another non-Amiga you can test on the router with it would be highly advantageous, modern routers won't usually config properly through an Amiga browser because they use Java applets or extensive Javascript. If you can't get the router to behave try yanking the power out of it and leaving it to stand for 5 mins and re-powering it, this won't clear the settings but hopefully it'll rescue it if it's locked up. Lock-ups on cheap routers are very common due to poor quality and manufacture and bad design, which causes overheating and instability. No computer is ever perfectly stable but a decent quality router will go for months rather that days without a reset.
If you can't get it to work properly on a wired network then you can always get hold of a prism2 compatible wireless PCMCIA card and try it that way.
