DHD from Antarctica:
Battery was completely drained with no (known) way to recharge it.
DHD from off-world:
Definitely could have/should have, especially in the earlier years of the program. Didn't, probably because of worries of stranding people, but that fails the intelligence test (just "bury the gate" after they take the DHD). Maybe didn't because they weren't sure they could get it to work with our gate, but still should have been tried/mentioned in the series.
Continued "renting" due to political pressure AND the need for secrecy (Russian's threatened repeatedly to reveal the program to the world). So it was politically expedient to pay to keep the Russians quiet and the rentals provided a pseudo-legitimate way to do that.
A stripped down MALP would have been more than sufficient to carry a DHD back through an open Stargate, which doesn't require a DHD to maintain an open wormhole (see also: "manual dialing"). Alternatively, they could have taken the Antarctic DHD and swapped in a replacement power crystal from any of the many, many DHDs where the interface was blasted, but not the power crystal.
Out of universe: why spend the money to re-vamp their primary stage setting when what they had was working great already?