USB Hub

I need some advice regarding usb hubs. My laptop is a Fujitsu Siemens Amilo li2735 which had 4 usb ports when it was new. Unfortunately where I was living at the time was pretty cramped so I had things on top of the wardrobe. Something fell down and buckled a couple of usb dongles. The dongles, one for internet connection and the other for wireless mouse, were total write offs. So were the two ports that I was using at the time.
I still have the other two but it isn't quite enough so I use usb hubs. I was wondering if anyone can give me a little advice about beefing up my plug-in capasity. I have searched other forums and read what replies others had received with the same kind of usb hub questions. In fact the more I read, the more confused I became. i would like to avoid if at all possible extra cables from a powered hub. I've already got too many cables as it is. Can I realistically expect to manage with a non powered hub.
I have 2 working ports and two damaged ones, and I need 3 connections. I have a hub that I purchased from a major supermarket, a non powered hub but sometimes it works ok but then it stops. The one I have is marked as; usb 20 hi-speed 4 port mini hub.
I know this is not urgent, but I would be greatful if anyone can advise me what I need to get, thank you.