Sony, Canon, Panasonic
These are the 3 most reliable brands i see sold.
Had 6 sony compacts in the house so far, not had one problem with them, downside being they use Pro Duo, which is over priced and unlikely to work with anything else of yours. Info Lithium Batteries are an excellent idea, which dont more brands do this!
The Canons are a bit bulky for what they are and low light performance is not as good as i would expected. But well put together and very rarely see problems with them.
The panasonics ive never owned, but having used them for ages at work they seem the best put together, well thought out. The larger models have quite a weight to them, but they seem to hold their own at the longer optical 'zooms'
Im not sure for a compact you couldnt go too far wrong with any of the above.