Hey there QG,
Twitter is just a website and it's not even a very demanding one at that so the power of your computer is unlikely to be the cause of the issue! Browsing the web requires very little raw computer power.
The first thing to do is to try an alternative browser Internet Explorer isn't a particularly effective browser although it has improved considerably over the last two versions.
There are four main alternative which are popular Firefox, Chrome, Opera and Safari different people have different preferences.
My order of preference is...
Firefox it's secure and has a vast range of plugins available.
Opera is clean and minimalist I only really use it for testing so I can't say what it's like to use all the time.
Chrome is very responsive but is own and controlled by Google, which helps them gain more dominance of the worlds data and people machines. Which long term is a dangerous situation no matter how fluffy they portray their business principles to be IMHO. I wouldn't and don't trust google period.
Safari I can't really comment on because I only ever use it for testing how it renders a page.
I.E is mind numbingly slow and the least stable browser in my experience and it's own by microsoft which is just as bad as google chrome when it comes to personal security and privacy much like chrome.
Maxthon I'm not familiar with.
If you visit this page
Browser Choice you will have easy access to download and install an alternative browser of your choice. Once you have installed one try using Twitter and see what the result you get.
It may also be a good idea for you to do some security scans on your computers because the issue your experiencing doesn't sound normal.