But it works fine on the other computer. Could it still be my ISP?
It could, unless your other computer is identical in all respects, then you are not comparing apples and apples.
Have you tried the wired ethernet adapter just to narrow the issue down to the wireless connection?
Have you tried the laptop at another location, friends, neighbors, relatives, coffee shop or other hotspot, to perhaps zero in on your wireless router?
Manufacturer name, model name, model number and rev number of both adapters may help us provide further assistance regarding a possible driver update.
You may also want to check the router manufacturer's website and see if they have a firmware update that might address the problem. They often include...