The biggest problem Deaf people have historically had is a lack of access to information. Deafness itself causes a lack of access to overheard information and radio, and poor educational standards for deaf kids have historically caused lower reading skills, meaning that TV captions and/or newspapers are less accessible than they are for hearing people.

Regarding the HIV epidemic, this manifested in higher infection rates due to lack of information about safer sex practices and other forms of protection (eg, clean needles). In the 1980s and 1990s, information was frequently shared from person to person, which resulted in it becoming distorted. Indeed, studies in 1997 and 2001 found that deaf students had a lot less knowledge of HIV transmission, and a lot more errors in the knowledge they did have.^1, ^2

The earliest program I know of to support the Deaf community getting more information was the [Deaf AIDS Center], founded in the Bay Area in 1986. Deaf AIDS Project was founded in Maryland in 1990. (I believe the Center closed about 10 years ago, but I am pretty sure DAP is still running.) There have also been a number of other efforts for education around the country,^3 but none of these organizations were ever terribly well-funded, I'm sorry to say - they did their best, but their impact was limited, simply by nature of not having the support to reach everyone.

The direct impact on the Deaf community was a significant loss of life. The Deaf Lost to AIDS list began in 1989, and today has hundreds of names. Many of the names on the list have panels on the NAMES quilt, which is searchable.

To this day, though, research shows that Deaf people have less knowledge than hearing people about public health.^4 HIV education for Deaf people seems to be improving thanks to the internet,^5 but the HIV epidemic is not over, and neither is the Deaf community's impact from it.

More sources:
The Nature of Risk: HIV/AIDS and the Deaf Community in the United States (Moinester et al, 2008)
Barriers to HIV/AIDS knowledge and prevention among deaf and hard of hearing people (Bat-Chava et al, 2007)
Deafness and HIV/AIDS: a systematic review of the literature (Hanass-Hancock and Satande, 2010)
Silence = Deaf (Friess, 1998)
Deaf activist with AIDS virus alerts others to danger (Bor, 1990)
HIV and AIDS among the deaf (Kennedy and Buchholz, 1995)