I can't log into my Chase account.

I can't log into my Chase bank account using my Mac and safari. I can using my iPhone and my iPad but not my Mac. I have tried calling Chase - no help - they said to call my internet provider - Time Warner. Time Warner spent a long time going through settings - they say it's Chase. I even called Apple and that was no help. I reset my MTU to 1472 under Systems Preferences per an older post in this community - and that didn't work. I even inserted my iMac OS X install disk and looked under utility to see if my disk needed repair. That didn't but my permissions did have some issues so I got that repaired. Still didn't work. I know it sounds like I know what I am doing, but I really don't. I am just following online directions. Does anyone have any suggestions? I just paid my bills online about 1 week ago and login worked. Time Warner did replace my internet router since then but they tell me that it seems as if Chase's system may be blocking the router??? HELP???