The problem with the ping pong sounds was not the screen, it was the webcam - it has a small connector that comes loose on some Inspirons (and older XPS's for that matter). Sometimes (not in your case) all it takes to "fix" it is to press firmly against the screen frame, one inch to the left or to the right of the webcam. This may reseat the connector (or pry it loose once and for all: dead webcam). For the "true" fix you need to carefully pry open the forward-facing screen frame in order to expose the webcam connector, and reseat it firmly with tweezers or needle-nosed pliers. A drop of Superglue will fix the connector forever and void the warranty, so you have to weigh your options.
The other symptoms you now have does seem like a short circuit and some component blown. But before buying the explanation (and a new laptop), you can try some manoeuvers:
verify that it boots neither on battery (even on a charged battery) nor on AC power.
with AC power and no battery, press and hold the power button for 30 seconds. It used to work on old Inspirons (medium-fresh ones like the 1730 require Fn key plus power). On some models you need the mute button plus Power.
if nothing happens, and hoping it's somehow the CMOS that got fritzed - maybe by that loose screw, who knows - try pulling out the CMOS battery to thoroughly zero them and force a new setup.
Apart from that, I'm afraid there's little one can do.
Update
Okay, I've been thinking over the various symptoms. Mohammad's hypothesis would be good, except that the laptop isn't stone cold dead; you do get a visual feedback:
Then if I press the power button the left most light (power) comes on
for 3 seconds. If I press it again I don't get the light again
The above could be caused by a configuration mismatch (and that's the CMOS). But there is maybe a simpler possibility: that you have partially displaced the power button panel connector when you removed the video cable.
- remove the power button panel
- open the power connector latch
- re-seat the connector
- close the latch again and reseat the panel.
Possibly, another connector that could be involved is the mainboard one which is near the display cable connector. Actually, were the problem there, my guess is that you should end up with a dead (albeit easily brought back to life) laptop. Just in case, check those two connectors as well.
(I'm not shooting down Mohammad's suggestion - actually I'm upvoting it - but it is a bit of a voodoo ritual. Mind you, I have performed such rituals myself, and they sometimes do work indeed. I just keep them last :-) ).
