Try running speed tests at various locations while on wired and wireless.
http://www.speedtest.net/
Wireless being spotty would have no effect your wired unless the router was foobar. It could be external issues to you (network issues or something). Or it could just be the router itself. You cannot just replace the fios router though, you still have to have it plugged in for TV if you have that. It is setup with coax usually and if you bridge your new router into the fios router, it will not solve your issue then. Would have to switch the service to ethernet I think or something and even then I am not sure.
I would try doing speed tests. I have 35/35 and sometimes when loading 1080p youtube vids, it is very very slow. So could just be Hulu sucking too.
One thing you could try is to unplug the router. Then also go over to the fios box inside with the battery and disconnect the battery then the power. Let it sit for a few minutes and plug it back in and reconnect the battery. Then turn back on the router. Make sure you are not planning on recording TV at that time

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