I have a HP Deskjet 648C that has problems...

I have fixed the noise that it was making (it was the color ink... it was leaking all over the connectors), but now I can't get the thing to print.

I know that it sounds like I had cleaned it and then it broke... it was doing this BEFORE I cleaned it. I have tried to print a test page, but no success there. What it does is that it seems like it is going to print. It takes the paper up from the tray and then it stops and the light (warning) starts flashing. I hae tried to correct this by pressing the button associated with the (warning) light, but that does nothing. Anyone have any ideas or clues?

Do you get the same error without any paper in the tray?
I have a feeling that the printer is not detecting that it has picked up the paper. You said that ink was leaking out all over the connectors. Maybe ink is clogging up the paper detect sensor, preventing it from working correctly?

I have tried to 'print w/o paper' and it does the same thing. I have already cleaned the connectors as much as I can and it still has the same problem. I have just contacted the HP service and they provided me with nothing but a headache.

The basic problem with HP printers is exactly what you are experiencing. The print head intermittently draws a lot of current (it actually boils the ink to print, like the Canon printers do) and any kind of dirt on the contact will cause it to error out. Further, if you bent a contact while cleaning, that nozzle element reads as an open circuit and will lead to the same error.

But I think such an error would show up BEFORE the printer would bother to pick up the paper, also it should have found that problem upon powerup when cleaning the jets

True, I guess I was confused. Maybe the ink gummed up something in the paper path. Thanks for pointing that out.

Then again, anything is possible...