Network Management Software

If it is one ISP that is causing the issue, you will need something to detect the downed line and switch to the other line.

Do a google search for "Dual WAN failover" or something similiar.

Here is an example of something that would help: "http://www.cisco.com/en/US/products/ps9926/index.html"

I did a failover/ISP swap on my firewall and the internet was still down, so it might be something on my LAN (or some device, or LAN card).

I don't know of any software that will tell you what exactly is causing your issue.

Best thing to do is troubleshoot.  When you have the problem, are you doing anything specific?  
Does the problem happen at a certain time on a certain day of the week?

There's no pattern so far, except that it usually happens around noon for about 5 or so minutes. It hasn't happened since I replaced my previous ISP with two new ISP's. I don't expect the software to tell me the cause of the issue. I just need it to point me in the right direction.

Wireshark is difficult to learn, and learning Wieshark may take a while. I need something thats easier to use or more user friendly. However, if you could give me directions on how to use Wireshark to achieve my stated purpose, I shall be grateful.

that is a very good indication that after ISP replacement you didn't have that problem. If i had similar issue, i'd start with router/firewall logs inspection. interface up/down, VPNs teared down anything in that nature will point to the link with ISP

If you run BGP, check that no bgp sessions were lost or anything strange happening around that time

another place to look is your spanning tree config, if it's not correct it could take about a minute for your switches to start forwarding when new link is introduced or something is changed.

add simple monitoring software and ping all devices on the path to the ISP (access switch, core switch, firewall internal and external interfaces, router internal and external interface, ISP end of your link(s), anything on internet). if that connection drop happen again, you should see where it stops and that will be a very good starting point for investigation

Avilov thanks for your insight. Please give me an example of such a simple monitoring software.

Wireshark is not difficult to use at all.  Interpreting your results takes some experience, but you have to use it to gain that experience.  If you have never done so I would highly recommend running some packet captures and start to become familiar with what is running over your network.  You might be surprised.

What does your network look like?  What switches/routers are you running?

I have a SonicWall NSA 3500 firewall as my lan gateway, and DHCP server. There are two 48-port Gigabit Netgear switches attached to the firewall (one switch is directly connected, while the other is daisy-chained to the other). All computers on my LAN, including the servers are connected to the two Netgear switched. On the WAN side, there is a Comcast Modem and a BOB internet CAT 6 cable, each directly connected to one WAN port, on the firewall.

your network is very simple, if it works 99.999% of the time, chances are that Comcast is doing something on their end. I wouldn't be surprised if they upgraded their modem firmaware when you had outages. it takes about 5 min to do that

problem is, even after I changed to another ISP, on my firewall, the internet was still down for a few minutes.