Can't login

We had a marketing company make our website for us. After they were done, I had asked for the login information so that I could have access to it, and was given the login information. I was able to login, change our password (for security purposes) and have remained logged on to our account on my current computer. However, I am unable to login on any other computer using the new password (or the old one for that matter). What’s going on? I don’t want to lose access to our website if I’m logged out of my computer! Please help!