"Modified Sine" outputs are very bad approximations of AC

This is a capture of the output of an APC 650 recorded by Jesse Kovach, while under load.

Notice the severe over-amplitude events at the extremes (the spikes at top and bottom). In reality they are actually much greater in amplitude, but the oscilloscope in the image was not fast enough to capture it.

Sharp edges in the time domain equate to broad-spectrum noise in the frequency domain. All of this high-frequency content represents additional energy that must be absorbed by protection circuits. If not, it can exceed isolation withstanding limits in the various input stage components and "burn through". If this doesn't burn out the input it will result in a cascading failure where it will cause something to fail on the secondary side from the resulting overvoltage.

...and that's just one failure mode. There are others. Psuedo-sine waves are poor matches to sine-wave inputs. :(

Go DC-DC instead of DC-AC-DC

A much better (and much more efficient!) approach is to go DC-to-DC directly (note: you can't actually go DC-to-DC directly if your input voltage is lower than your output voltage, but the details of this are well contained inside a "DC-DC converter").

Self-contained switch-mode power supplies for Dell laptops that take DC inputs are available in the marketplace. Here's an example:

which I sourced from:

http://www.amazon.com/Adapter-Charger-Dell-Latitude-D630/dp/B002BK7JEC#

Please note that I have no personal experience with this particular product and many cheap DC converters are poorly designed internally. Be careful.

The device, or circuit, you are looking for is called an inverter. You are right that it has a transformer connected backwards, but it also has a lot more besides. A block diagram of a typical inverter system might look something like this:

^{simulate this circuit – Schematic created using CircuitLab}

The H-Bridge is used by the controller system to generate an alternating current (AC) waveform. The transformer then steps the waveform up to the target voltage.

It's not a nice clean sine wave like you'd get from the mains, but instead what is called a "Modified Sine" wave (green line in this graph):

Due to limitations in the way the H-bridge works there has to be a gap (or dead zone) between driving in one direction and driving in the other. This gives the waveform its characteristic three-level appearance.

Inverters are not a very efficient system, since a proportion of the power is wasted as heat and even noise (they usually hum). It is far better to find a low voltage solution to your problem. Most appliances nowadays (excluding normal white goods) actually run on low voltages, and contain a power supply to reduce the voltage down to the typical 12V/5V/3.3V that you find everywhere now. A much better solution is to find products that allow you to bypass that power supply and provide the needed voltages (or a subset of them - typically 12V is used) directly to the device.