2 computers and one router vs one computer with wifi
i have a belkin router connected to one computer and other two wireless. However one of the two wireless computers (my dell xps 8500) has such bad connection with games. For example whenever i play league of legends the pings goes over 600 or more. And in online games the graphics are all smooth but it has delays like when attacking a monster its takes at least 3 seconds for my skills to activate or to have any of my basic attacks to come in contact with a monster. Im wondering if i should buy another internet cable and have it connect it to my belkin router which is already connected to my main computer or get a better router.
It is much cheaper to try the cable first. A "better" router will unlikely solve your problem. It would be very uncommon for the router itself to make much difference.
You likely have some form of wireless interference. Sometimes people get lucky because they set something different on the new router and think the router made the difference when it actually was something like running on a different channel that made the difference.
If you have the option to run cable for gaming you will always get much better results even if you would decide to buy a different router. Wireless tends to get periods of random interference even when it is working well. Games hate random network delays because they use the network timing to make predictions on location of items in games based on time.
You have 2 issues. The wireless is the common cause of high ping times and delays.
Running 2 computers does not matter how you connect them if one uses all the bandwidth and slows the other down it will do that no matter how you connect them. That is not a technical problem really you have to have a agreement which machine gets to use the internet when there is not enough.