Yes, you can certainly put in a claim.
The eligibility criteria for personal independence payment (PIP) are quite different to the criteria for disability living allowance (DLA), so some people who were refused an award of DLA may be eligible for PIP.
The fact that you have been refused DLA in the past should not generally be relevant to your PIP claim. However, if you have had a recent medical in relation to DLA it is possible that the medical report will be used as evidence when deciding your claim for PIP. In this case it is important that you distinguish any changes that have taken place since the DLA medical.