Losing Internet, Despite Wi-Fi and Router Connection

Question

A month after moving into a new apartment and setting up our internet, we began to have debilitating internet connection issues. We have a MacBook Pro 10.9.4, an iMac 10.6.8, two iPhone 5's and a PS3 that are wirelessly connect to our router, a Verizon Actiontec Model GT784WNV, on Verizon DSL Internet.
For no apparent reason after a month of use, all of our devices began regularly losing internet connection at once, multiple times a day---sometimes at two minute intervals. According to our computers, our Wi-Fi Network remained "Connected" and displaying a full signal when our browsers were unable to connect at all, and the wireless router showed a steady "Internet" connection light. Despite this, the only way to get the internet back has been by restarting the router.
It seems worth mentioning that during our repeated restarts of the router, both computers would occasionally (maybe every other day) alert us that "Another device on the network is using your computer's IP address" as we re-established our Wi-Fi conncection. Since our Wi-Fi is password protected, it only seems logical that it's the MacBook Pro and iMac causing problems for each other. Over the past two years, with similar DSL router setups and restarts, this never was a problem when re-establishing Wi-Fi connections on our computers. After doing some research to see if this might be our main issue, under Network>Advanced>Preferred Networks I removed and re-added the network on both computers, and confirmed they were set to Configure IPv4: "Using DHCP." This had no effect on our internet issue, although we've received less alerts now. For the most part, both computers seem to establish unique IP addresses whenever re-connecting to the Wi-Fi. Is this issue core to our problem, or just a coincidence?
I recently tried connecting our PS3 to the router via Ethernet cable while streaming Netflix to see if it'd stop dropping the Internet connection, but it turned out to be just as unreliable as wireless---to me this suggests that the router/ISP is the issue. We've also tried turning off Wi-Fi on all but one device, but it eventually loses connectivity as well.
I'm wondering if this suggests a issue with our computer settings, or if I need to be in touch with our ISP in regards to a faulty router or intermittent internet? Any insight or suggestions would be a huge help, thanks so much!

Answer 1

You're going to be troubleshooting this and probably eventually discussing this with Verizon.
In the typical small dynamic-IP network setup, the WiFi router gets its address from Verizon via DHCP, and the WiFi router then issues "private" addresses to your clients via its own DHCP server.
Restarting the WiFi router can cause address collisions, as the cheaper WiFi routers don't probe for existing clients and just start handing out addresses and this quite possibly leads to address collisions.   The smarter WiFi routers will probe the network and determine if an IP address is already in use, and will then avoid passing it out again.
if your WiFi router supports it, I'd look to move to 5 GHz — from what I can tell from what few specs available, it doesn't appear to support 5 GHz — as the 2.4 GHz band tends to be heavily used in apartment buildings and built-up areas, and with excessive interference resulting.  (Though your attempts to use a hard-wired connection imply a problem with the WiFi router or with the DSL.)