Citation Captain reports the inability to move the landing gear handle to the up position after takeoff. During troubleshooting; the flight is assigned 6;000 FT; but the First Officer sets 8;000 FT mistakenly. ATC questions the altitude at 7;400 FT.

Narrative

We departed from ZZZZ to ZZZ1 with 2 crew and 4 passengers. The plane sat for 7 days [prior]. Takeoff [was] normal until gear up was called. The gear handle would not move to the up position. Tower switched us over to Departure who gave us a climb to 10;000 FT. Departure was advised we had a problem with our landing gear. Also; we requested radar vectors and a lower altitude in an attempt to fix our problem. Departure assigned us 6;000 FT. Copilot read back 6;000 FT to ATC; set altitude; and again reported he had set 6;000 FT to me over the headset. However; he had set 8;000 FT and called 6;000 FT. This copilot is low time and less than 100 hours in type. I had turned the airplane over to the copilot while I attempted to fix our problem. With the gear extended; we would not be making a 1;200 mile flight. ATC questioned our altitude and asked [if] we were still planning on climbing to 10;000 FT. The mistake was discovered at 7;400 FT. ATC stated the deviation was not a problem; knowing we had gear problems and were attempting to find a fix. Many lessons were learned from this mistake. We are looking into procedures in hopes that this sort of mistake will never happen again.