You should contact a Realtor in the Pittsburgh area to help you determine if you can qualify for a loan, and if so, the amount you can qualify for. If you don't qualify, then you will have provide proof of income that you can pay cash. Howard Hanna Real Estate Services provides these services "in house," so if you contact an agent, we can find out what you qualify for right away.
Before making a decision to buy, talk to a reputable credit counselor. I recommend Advantage Consumer Credit Counseling Service: http://www.advantageccs.org. No sense in buying for cash, if a creditor will slap on a lien and foreclose. You also want to become a successful homeowner, not a homeowner in trouble. Also, browse for fillable Form RD 1944-3, a government household budget, at: http://forms.sc.egov.usda.gov/efcommon/eFileServices/eForms/ Fill it out completely and it will tell you what you can and cannot afford. When you are ready to buy, start with something that is affordable, but also in good shape and not needing a lot of repairs.
If you are not able to use cash as Michael suggested in the previous post, you will want to talk with a lender about a mortgage. You may want to try talking to US banks that have branches in the UK...they may be more open to an international purchase mortgage.
Sure, in your situation, the best and most likely scenario is for you to buy a house for your wife in Pittsburgh with all cash. Given the low prices there, that's less of a hurdle than many other cities.