Can a person who has a plaster cast, and is unable to do ghusl, do tayammum?
Question

I had surgery on my knee joint and they put a plaster cast from the top to the bottom of my leg. During the first few days I could not even sit up, and I had a wet dream. Do I have to do ghusl, or is tayammum sufficient? I prayed for two days with tayammum, then I asked my relatives to wash me (ghusl), but then I had a wet dream on the second day, and it is very difficult for my relatives to wash me, so I waited a few days before they could do that. Are my prayers offered with tayammum valid?.
Praise be to Allah.Firstly: 
In the answers to questions no. 69796 and 148062, we mentioned the ruling on wiping over a part of the body that is covered with a plaster cast, bandage or dressing, in which it says: 
The part of the body that is covered with any of the things we have mentioned, or anything similar, is to be wiped over if it is possible to do that without causing any harm, whether in wudu or ghusl. If the part of the body is not covered, then it should be washed if possible. If that is not possible because it will result in harm such as increased pain or sickness, or delayed healing, then it should be wiped over. If he cannot do either, then he should wash the parts that he is able to wash – in both wudu and ghusl – and do tayammum, after he has finished washing with water, for that part that the water could not reach. End quote. 
Based on that, what you have to do when doing ghusl is to wash all of your body with water, except the part where the plaster cast is; it is sufficient to wipe over. Thus your ghusl will be complete and there will be no need for tayammum. 
Secondly: 
Because you mentioned in your question that it is very difficult to go to the bathroom to do ghusl, there is nothing wrong with you doing tayammum, because tayammum is an alternative to doing ghusl with water when there is a legitimate shar‘i excuse for that. Allah, may He be exalted, mentioned sickness as one of the reasons that make tayammum permissible, as He said (interpretation of the meaning):
“And if you are ill, or on a journey, or one of you comes after answering the call of nature, or you have been in contact with women (by sexual relations) and you find no water, perform Tayammum with clean earth and rub therewith your faces and hands (Tayammum). Truly, Allah is Ever Oft-Pardoning, Oft-Forgiving”
[an-Nisa’ 4:43]. 
In this case you have to wash whatever you can of your body, such as the face, head and hands, then do tayammum after that. 
Shaykh Saalih al-Fawzaan – may Allah preserve him – said: If a person is not able to purify himself with water at all, or it is extremely difficult for him and he cannot find someone to help him, there is nothing wrong with him doing tayammum using dust, because Allah, may He be exalted, says (interpretation of the meaning):
“And if you are ill, or on a journey, or one of you comes after answering the call of nature, or you have been in contact with women (by sexual relations) and you find no water, perform Tayammum” [an-Nisa’ 4:43]. 
In al-Maa’idah 5:6, Allah, may He be glorified and exalted, mentions sickness as one of a number of excuses which make it permissible to do tayammum. And Allah says (interpretation of the meaning):
“So keep your duty to Allaah and fear Him as much as you can” [al-Taghaabun 64:16].
End quote from al-Muntaqa min Fatawa ash-Shaykh al-Fawzaan, 5/23 
Shaykh ‘Abdullah ibn Jibreen (may Allah have mercy on) was asked: 
There is a girl who was put under anaesthetic in the hospital for a number of days so that an operation could be carried out on her. She said: When I went into hospital I was not praying because I had my monthly period. Then it stopped whilst I was in the hospital and I am not able to do ghusl in the hospital. What should I do? Is it sufficient for me to intend ghusl in my heart or what? Please advise me. 
He replied: 
She is excused so long as she is undergoing surgery or is in the hospital bed and is not able to do ghusl. It is sufficient for her to do tayammum using dust or on the bed if she cannot find any dust, and she may do tayammum for minor impurity, in place of wudu, if she is not able to do that. If she is able to go into the bathroom and close the door behind her, then she has to do ghusl, because she is able to do so without difficulty. But if she is not able to reach the bathroom because of the surgery and because she has to stay in bed, then tayammum is sufficient because of the difficulty involved (in doing ghusl or wudu). End quote. 
Then when Allah, may He be exalted, heals you, you have to do ghusl. 
We ask Allah to bless you with a quick recovery. 
And Allah knows best.