I know it sounds nuts, but unless you are willing to go a quite complicated route involving USSD codes from your datacard or modem, or want to drill through pages on the MTN site, the short answer seems to be: forget it, it's not worth the hassle, just do it through your cellphone!
I went through exactly the same realisation curve a couple of weeks back, discovering eventually (through this Forum) that the easiest way really is to simply take out your SIM card, slap it into a cellphone and hit *141#. Yes, cumbersome given the ease with which you can get your balance direct from your datacard with Vodacom, but it's a glaring omission MTN just doesn't seem to be interested in addressing despite what must now be many thousands of people getting data online from it using datacards or modems.
(Be aware though that if you are on Contract, the balance you will get through *141# -- or the website -- could be up to 24 hours behind. Prepaid seems to be fairly current. Another weird quirk).
Yes, if you want a balance directly from your datacard or modem, you could try the code route mentioned in other threads in this forum, using Hyperterminal and the like, but honestly, it's more trouble than it's worth unless you are an inveterate fiddler and like spending half an hour to do something which will only take you a minute whacking the data SIM into a cellphone....