Does my unemployment affect my petition for my parents i130 visa?

At the time you need to show support (affidavit of support) you will need to either have sufficient income and/or assets or have a joint sponsor to sign the affidavit of support on your parents' behalf. Please let me know if you have any additional questions or how I can be of further assistance to you in this matter.

It can have an effect if you do not meet the proper income requirements.

The USCIS processing time in your category is about 7 months. After that, the case will go to the National Visa Center, which will send you a letter asking for visa fees and visa applications. After you submit everything requested by NVC, it will forward the file to the US Embassy in your parents' country. The Embassy will invite your parents for an interview. Depending on the country, the entire process can take from one year to 18 months. Make sure that your income from the new job still qualifies you to maintain affidavit of support (it means that your income must be above 125% of the federal poverty guidelines; if you have no dependents, you have to count yourself and your parents (3 persons) and your income has to be over $23,863; if you do have 1 dependent (a child, a non-working spouse, etc.) the min. income is $28,813; 2 dependents - $33,763; and so on) Be ready to send documents proving your current employment (a company letter confirming your employment will do) and your current income (paystabs for 5-6 weeks usually suffice) to USCIS (if they ask for it), or to your parents (to show to the consular officer at the interview, if requested). If your income is smaller than the poverty guidelines require, you need to find a co-sponsor and file a second affidavit of support, or use your assets, or use the income of a family member who lives with you. If you have to resort to one of these options, I would recommend asking an immigration attorney to help, because a mistake in preparing the necessary papers will result in denial of your petition, and re-filing will cost you more than an attorney's fee on such a case.

Unemployment will not affect I-130, but can affect I-485.

The answer to your question is no, if current income from the new job meets the minimum of 150% of the federal poverty line that applies to you. If your parents are going to apply for immigration visas from back home (I think that's your situation?), the process takes about 9 months.