Although I can't for the life of me figure out what is different about the second "hello there", the best thing to do when you have keyboard issues is to test the computer with a different keyboard. If it works properly, then you know what's at fault.
If you consider yourself handy at electronic repairs, you could open up the keyboard and disassemble enough to get at the contact points for the space bar. Usually they look like part of a large array of printed-circuit traces in black carbon, and they are touched by a carbon button when the space bar is pushed. I'm guessing the contacts, either on the space bar itself or on the contact sheet, are dirty. Clean them gently - a pink pencil eraser works well - followed by a gentle wipe with a clean tissue (or brush with a soft painter's brush) to remove dust. Reassemble and see if it's better.
The reason no one sees a difference between the two "hello there" lines is because HTML reduces all whitespace, including tabs and carriage returns/linefeeds (enter key) into a single space character. When you hit enter in the textbox, the script on the server adds a <br /> to the HTML. It doesn't turn all the spaces into , though, so two spaces is rendered as one space. If you View Source on the page, then you can see the difference between the two "hello there" lines.
either buy a new keyboard or everytime you hit the space bar hit the backspace key to get rid of the added space. i think the former rather than the latter would be best.