Even experienced people are finding it difficult to find work due to market conditions and you need to be both realistic and flexible. It is true that experience is important and getting this experience can initially be an uphill struggle. Often the most senior people in IT started at the bottom and had no formal qualifications, so do not let the fact that you have no degree hold you back. Bill Gates never finished his course so you are one up on him.
An HND in chemistry and computing and your diploma in C programming, alongside the additional qualifications you are studying for, should provide a solid foundation. However, putting these skills into practice is the real test and understandably employers are looking to take on candidates with a proven track record.
Although your previous job did not work out, there are some strong hints to be taken from the experience. Always try to find out as much as possible about the job you are taking on and do not oversell yourself. It is also a good idea to try and find out as much as you can about why the job did not work out. Exit interviews are now common practice and these can help both the employer and the individual to get a better idea about how they need to change the way they work. In terms of future prospects be prepared to set your sights on realistic job targets - if you do succeed in getting a job that is asking for two to three years experience then you are likely to encounter similar problems to your last job.