Corrected entry: Carter and O'Neil get trapped on a planet where the DHD does not work, they say that eventually they may get rescued by another team, however if the other team gets there then how are they themselves supposed to get back since they cannot dial home and neither can SGC dial up to them since it is said countless times that you cannot go through a wormhole unless you dialed it, i.e. it is a one way thing.
Corrected entry: The DHD of the second Stargate can be seen. It has a point of origin different to that from the gate found in Gizeh. However, after SGC starts using the Antarctican gate at the end of season 3 the glyph indicating the point of origin on the gate and in the computer systems is still as seen on the gate from Gizeh.
Correction: Point of origin is not an aspect of the gate or the DHD. The pyramid with the circle on top is the symbol for Earth. The gates found in both Giza and Antarctica use the same symbol. Carter originally thought the one in Antarctica used a different one because she thought they were not on Earth.
This correction is inaccurate. Every gate and DHD has their own unique point of origin. There's no reason for the Antarctica gate to have the same point of origin as the Giza gate, which was brought from another planet by the Goa'uld. Also, the Antarctica gate's DHD was shown with its own unique point of origin in "Solitudes." It was a filled in circle with a line under it (google image: antartica gate point of origin). When the SGC used the beta gate they ignored that and continued to show the Giza gate's pyramid + sun symbol. Doing so directly contradicted what we had seen before and what we were told about point of origins and therefore is a legitimate goof.
Correction: But when dialing a world, they always send a probe through first to make sure it is safe and if there is a DHD, so when they send the probe, they could radio the SGC and tell them the DHD is broken which could then be fixed or replaced.
Craig Bryant
Just to add to this: Several episodes established that the protocol for situations where the DHD isn't working is to wait for the SGC to check in on them. Once the SG team explains the problem, over radio, the SGC will send over a portable power source. All they have to do then is hook it up and manually dial the gate to get home. In later seasons, they talk about how the SGC can send a naquadah generator and laptop with the dialing program installed on it.