I have a Gateway GT5628 that's not booting up at all. I press the power button, and it all lights up. But it doesn't load up anything on the screen. I opened up the the computer and cleaned up all the dust and stuff, but it still doesn't work.

One thing I do notice is that the case fan in the back is spinning pretty slow. I'm not sure if its the power supply. I tried another power supply but that didin't boot it up either. Solutions or ways to check way the problem is?

I'm not sure exactly what the issue is from your description but can I suggest trying these steps.

unplug the vga/DVI cable from the monitor and check for the monitor's self test feature which means it goes from standby to on- make sure your not overlooking a monitor issue here.

Look out for the bios reset on the motherboard that should resolve any CMOS corruption issues- one of the symptoms could be a slow system fan. -http://support.gateway.com/s/MOTHERBD/Intel2/4006194R/4006194Rmvr24.shtml

finally- check the keyboard lights(you know- caps lock, scroll lock - num lock) make sure they toggle on and off -these can indicate that your system is processing fine and it might just be a video issue.

let me know how you get on.