Is this what your motherboard looks like?
http://www.ebay.ca/itm/Dell-Vostro-270-Inspiron-660-Motherboard-0478VN-11061-1-DIB75R-XFWHV-478VN-/262023140387
Looks like standard PSU connections, which should make replacing the PSU an easy enough task.
I can't find any information on the form-factor though. Many listings state it's an ATX board, but it's clearly not. Looks more like a mITX board to me (but whether it's a 'standard' form board that'll fit another case, I can't tell).
Also, look at your CPU cooler - does it mount to the case directly? Or to a backplate on the motherboard?
If it attaches through the board, and secured into the case itself (as some Dell's do), then you'll need to source a new cooler.